Cross derivative of γ^o with respect to π and temperature τ
Values for calculation
Calculation
Cross derivative of γ^o with respect to π and temperature τ
\text{if }\ \text{Region}= 2γ^o_{πτ}=0
γ^o_{πτ}=0
γ^o_{πτ}=0
| Name | Mathematical constant | Value | Notation |
|---|---|---|---|
| One | 1 | 1 | M_ONE |
| Two | 2 | 2 | M_TWO |
| One half | 1/2 | 0.5 | M_ONE_HALF |
| Ludolph's number | π | 3.1415926535898 | M_PI |
| Tau | τ=2\cdot π | 6.2831853071796 | M_TAU |
| Euler's number | e=\sum_{n=0}^{\infty}\cfrac{1}{n!}=1+\cfrac{1}{1}+\cfrac{1}{1\cdot 2}+\cfrac{1}{1\cdot 2\cdot 3}+\cdots | 2.718281828459 | M_E |
| Euler's constant | γ=\lim_{n\rightarrow\infty}\left(-\log{n}+\sum_{k=1}^{n}\right)\cfrac{1}{k} | 0.57721566490153 | M_EULER |
| Apéry's constant | ζ(3)=\sum_{n=1}^{\infty}\cfrac{1}{n^3}=1+\cfrac{1}{2^3}+\cfrac{1}{3^3}+\cfrac{1}{4^3}+\cfrac{1}{5^3}+\cdots | 1.2020569031596 | M_APERY |
| Catalan's constant | G=\sum_{n=0}^{\infty}\cfrac{\left(-1\right)^n}{\left(2n+1\right)^2}=\cfrac{1}{1^2}-\cfrac{1}{3^2}+\cfrac{1}{5^2}-\cfrac{1}{7^2}+\cfrac{1}{9^2}-\cdots | 0.91596559417722 | M_CATALAN |
| Feigenbaum constant α | α | 2.5029078750959 | M_FEIGENBAUM_ALPHA |
| Feigenbaum constant δ | δ | 4.669201609103 | M_FEIGENBAUM_DELTA |
| Lemniscate constant | ϖ=2\int_{0}^{1}\cfrac{\text{d}t}{\sqrt{1-t^4}} | 2.6220575542921 | M_LEMNISCATE |
| Glaisher–Kinkelin constant | A | 1.2824271291006 | M_GLAISHER |
| Khinchin's constant | K_0=\lim_{n\rightarrow\infty}\left(a_1a_2\ldots a_n\right)^{1/n} | 2.6854520010653 | M_KHINCHIN |
| Golden Ratio | φ=\cfrac{1+\sqrt{5}}{2} | 1.6180339887499 | M_GOLDEN_RATIO |
| Silver Ratio | δ_S=\sqrt{2}+1 | 2.4142135623731 | M_SILVER_RATIO |
| Supergolden Ratio | ψ=\cfrac{1+\sqrt[3]{\cfrac{29+3\cdot\sqrt{93}}{2}}+\sqrt[3]{\cfrac{29-3\cdot\sqrt{93}}{2}}}{3} | 1.4655712318768 | M_SUPERGOLDEN_RATIO |
| Connective constant | μ=\sqrt{2+\sqrt{2}} | 1.8477590650226 | M_CONNECTIVE |
| Kepler–Bouwkamp constant | K'=\prod_{n=3}^{\infty}\cos\left(\cfrac{π}{n}\right)=\cos\left(\cfrac{π}{3}\right)\cos\left(\cfrac{π}{4}\right)\cos\left(\cfrac{π}{5}\right)\cdots | 0.1149420448533 | M_KEPLER_BOUWKAMP |
| Erdős–Borwein constant | E=\sum_{n=1}^{\infty}\cfrac{1}{2^n-1}=\cfrac{1}{1}+\cfrac{1}{3}+\cfrac{1}{7}+\cfrac{1}{15}\cdots | 1.6066951524153 | M_ERDOS_BORWEIN |
| Omega constant | Ω=\cfrac{1}{π}\int_{0}^{π}\log\left(1+\cfrac{\sin t}{t}e^{t \cot t}\right)dt | 0.56714329040978 | M_OMEGA |
| Gauss's constant | G=\cfrac{1}{\text{agm}\left(1, \sqrt{2}\right)}=\cfrac{1}{4π}\sqrt{\cfrac{2}{π}}Γ\left(\cfrac{1}{4}\right)^2=\cfrac{ϖ}{π} | 0.83462684167407 | M_GAUSS |
| Second Hermite constant | γ_2=\cfrac{2}{\sqrt{3}} | 1.1547005383793 | M_SECOND_HERMITE |
| Liouville's constant | L=\sum_{n=1}^{\infty}\cfrac{1}{10^{n!}}=\cfrac{1}{10^{1!}}+\cfrac{1}{10^{2!}}+\cfrac{1}{10^{3!}}+\cfrac{1}{10^{4!}}+\cdots | 0.110001 | M_LIOUVILLE |
| Ramanujan's constant | {e}^{π\cdot\sqrt{163}} | 2.6253741264077E+17 | M_RAMANUJAN |
| Dottie number | D | 0.73908513321516 | M_DOTTIE |
| Meissel-Mertens constant | M=\lim_{n\rightarrow\infty}\left(\sum_{p\le n}\cfrac{1}{p}-\ln\left(\ln n\right)\right)=γ+\sum_{p}\left(\ln\left(1-\cfrac{1}{p}\right)+\cfrac{1}{p}\right) | 0.26149721284764 | M_MEISSEL_MERTENS |
| Universal parabolic constant | \ln{\left(1+\sqrt{2}\right)}+\sqrt{2} | 2.2955871493926 | M_UNIVERSAL_PARABOLIC |
| Cahen's constant | C=\sum_{k=1}^{\infty}\cfrac{\left(-1\right)^k}{s_k-1}=\cfrac{1}{1}-\cfrac{1}{2}+\cfrac{1}{6}-\cfrac{1}{42}+\cfrac{1}{1806}\pm\cdots | 0.64341054628834 | M_CAHEN |
| Gelfond's constant | {e}^π | 23.140692632779 | M_GELFOND |
| Gelfond-Schneider constant | 2^{\sqrt{2}} | 2.6651441426902 | M_GELFOND_SCHNEIDER |
| Second Favard constant | K_2=\cfrac{π^2}{8} | 1.2337005501362 | M_SECOND_FAVARD |
| Golden angle | g=π\cdot\left(3-\sqrt{5}\right) | 2.3999632297287 | M_GOLDEN_ANGLE |
| Sierpiński's constant | K=π\left(2γ+\ln\cfrac{4π^3}{Γ\left(\cfrac{1}{4}\right)^4}\right)=π\left(2γ+4\ln Γ\left(\cfrac{3}{4}\right)-\ln π\right)=π\left(2\ln2+3\ln π+2γ-4\ln Γ\left(\cfrac{1}{4}\right)\right) | 2.5849817595793 | M_SIERPINSKI |
| Landau-Ramanujan constant | b=\cfrac{1}{\sqrt{2}}\prod_{p\equiv 3\ (\mod 4)}\left(1-\cfrac{1}{p^2}\right)^{-\cfrac{1}{2}}=\cfrac{π}{4}\prod_{p\equiv 1\ (\mod 4)}\left(1-\cfrac{1}{p^2}\right)^{\cfrac{1}{2}} | 0.76422365358922 | M_LANDAU_RAMANUJAN |
| First Nielsen-Ramanujan constant | a_1=\cfrac{π^2}{12} | 0.82246703342411 | M_FIRST_NIELSEN_RAMANUJAN |
| Gieseking constant | G=\cfrac{3\sqrt{3}}{4}\left(1-\sum_{n=0}^{\infty}\cfrac{1}{\left(3n+2\right)^2}+\sum_{n=1}^{\infty}\cfrac{1}{\left(3n+1\right)^2}\right)=\cfrac{\sqrt{3}}{4}\left(\cfrac{ψ_1\left(1/3\right)}{2}-\cfrac{π^2}{3}\right) | 1.0149416064097 | M_GIESEKING |
| Bernstein's constant | β=\lim_{n\rightarrow\infty}2nE_{2n}\left(f\right) | 0.28016949902387 | M_BERNSTEIN |
| Tribonacci constant | \cfrac{1+\sqrt[3]{19+3\cdot\sqrt{33}}+\sqrt[3]{19-3\cdot\sqrt{33}}}{3} | 1.8392867552142 | M_TRIBONACCI |
| Brun's constant | B_2=\sum_{p}\left(\cfrac{1}{p}+\cfrac{1}{p+2}\right)=\left(\cfrac{1}{3}+\cfrac{1}{5}\right)+\left(\cfrac{1}{5}+\cfrac{1}{7}\right)+\left(\cfrac{1}{11}+\cfrac{1}{13}\right)\cdots | 1.902160583104 | M_BRUN |
| Twin primes constant | C_2=\prod_{p\ \text{prime,}\ p\geq3}\left(1-\cfrac{1}{\left(p-1\right)^2}\right) | 0.66016181584687 | M_TWIN_PRIMES |
| Plastic Ratio | ρ=\sqrt[3]{\cfrac{1}{2}+\cfrac{\sqrt{69}}{18}}+\sqrt[3]{\cfrac{1}{2}-\cfrac{\sqrt{69}}{18}} | 1.3247179572447 | M_PLASTIC_RATIO |
| Prouhet-Thue-Morse constant | τ=\sum_{n=0}^{\infty}\cfrac{t_n}{2^{n+1}}=\cfrac{1}{4}\left[2-\prod_{n=0}^{\infty}\left(1-\cfrac{1}{2^{2^n}}\right)\right] | 0.41245403364011 | M_PROUHET_THUE_MORSE |
| Golomb-Dickman constant | λ=\int_0^1e^{Li\left(t\right)}dt=\int_0^{\infty}\cfrac{ρ\left(t\right)}{t+2}dt | 0.62432998854355 | M_GOLOMB_DICKMAN |
| Lebesgue constant | c=\lim_{n\rightarrow\infty}\left(L_n-\cfrac{4}{π^2}\ln\left(2n+1\right)\right) | 0.98943127383115 | M_LEBESGUE |
| Feller-Tornier constant | C_{FT}=\cfrac{1}{2}\prod_{p\ \text{prime}}\left(1-\cfrac{2}{p^2}\right)+\cfrac{1}{2} | 0.66131704946962 | M_FELLER_TORNIER |
| Champernowne constant | C_{10}=0.1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9\ 10\ 11\ 12\ 13\ 14\cdots | 0.12345678910111 | M_CHAMPERNOWNE |
| Salem constant | σ_{10}=x^{10}+x^9-x^7-x^6-x^5-x^4-x^3+x+1 | 1.1762808182599 | M_SALEM |
| Lévy's constant | β=\cfrac{π^2}{12\cdot\ln{2}} | 1.1865691104156 | M_LEVY |
| Copeland-Erdős constant | C_{CE}=0.2\ 3\ 5\ 7\ 11\ 13\ 17\ 19\ 23\ 29\ 31\ 37\cdots | 0.23571113171923 | M_COPELAND_ERDOS |
| Mills' constant | \left\lfloor A^{3^n}\right\rfloor | 1.3063778838631 | M_MILLS |
| Gompertz constant | δ=\int_0^{\infty}\cfrac{e^{-x}}{1+x}dx | 0.59634736232319 | M_GOMPERTZ |
| Van der Pauw constant | \cfrac{π}{\ln{2}} | 4.5323601418272 | M_VAN_DER_PAUW |
| Magic angle | θ_m=\tan^{-1}{\sqrt{2}} | 0.95531661812451 | M_MAGIC_ANGLE |
| Artin's constant | C_{Artin}=\prod_{p\ \text{prime}}\left(1-\cfrac{1}{p\left(p-1\right)}\right) | 0.3739558136192 | M_ARTIN |
| Porter's constant | C=\cfrac{6\ln 2}{π^2}\left(3\ln 2+4γ-\cfrac{24}{π^2}ζ'\left(2\right)-2\right)-\cfrac{1}{2} | 1.467078079434 | M_PORTER |
| Lochs constant | L=\cfrac{6\ln 2\ln 10}{π^2} | 0.97027011439203 | M_LOCHS |
| Lieb's square ice constant | \left(\cfrac{4}{3}\right)^{\cfrac{3}{2}} | 1.539600717839 | M_LIEB_SQUARE_ICE |
| Niven's constant | C=1+\sum_{n=2}^{\infty}\left(1-\cfrac{1}{ζ\left(n\right)}\right) | 1.7052111401054 | M_NIVEN |
| Stephens' constant | C_S=\prod_{p\ \text{prime}}\left(1-\cfrac{p}{p^3-1}\right) | 0.57595996889295 | M_STEPHENS |
| Zero | 0 | 0 | M_ZERO |
| Negative one | -1 | -1 | M_NEGATIVE_ONE |
| Square Root of 2 | \sqrt{2} | 1.4142135623731 | M_SQRT2 |
| Square Root of 3 | \sqrt{3} | 1.7320508075689 | M_SQRT3 |
| Square Root of 5 | \sqrt{5} | 2.2360679774998 | M_SQRT5 |
| Cube Root of 2 | \sqrt[3]{2} | 1.2599210498949 | M_CURT2 |
| Cube Root of 3 | \sqrt[3]{3} | 1.4422495703074 | M_CURT3 |
| Twelfth Root of 2 | \sqrt[12]{2} | 1.0594630943593 | M_TWRT2 |
| Natural Log of 2 | \ln(2) | 0.69314718055995 | M_LN2 |
| Natural Log of 10 | \ln(10) | 2.302585092994 | M_LN10 |
| Natural Log of Pi | \ln(π) | 1.1447298858494 | M_LNPI |
| Base 10 Log of e | \log10(e) | 0.43429448190325 | M_LOG10E |
| Base 2 Log of e | \log2(e) | 1.442695040889 | M_LOG2E |
| Half of Pi | π/2 | 1.5707963267949 | M_PI_2 |
| Quarter of Pi | π/4 | 0.78539816339745 | M_PI_4 |
| Inverse of Pi | 1/π | 0.31830988618379 | M_1_PI |
| Two over Pi | 2/π | 0.63661977236758 | M_2_PI |
| Square Root of Pi | \sqrt{π} | 1.7724538509055 | M_SQRTPI |
| Two over Square Root of Pi | 2/\sqrt{π} | 1.1283791670955 | M_2_SQRTPI |
| Inverse of Square Root of 2 | 1/\sqrt{2} | 0.70710678118655 | M_SQRT1_2 |
| Function | Description | Sample example |
|---|---|---|
| ABS | Returns the absolute value of a number. The absolute value of a number is the same number without a sign. | ABS(-9)=9 |
| ACCRINT | Returns the total interest on securities that pay interest on regular dates. | ACCRINT(39508, 39691, 39569, 0.1, 1000, 2, 0)=16.666666666667 |
| ACCRINTM | Returns the accrued interest on a security that pays interest on the maturity date. | ACCRINTM(39539, 39614, 0.1, 1000, 3)=20.547945205479 |
| ACOS | Returns the arccosine (the inverse of the cosine function) of the specified number. The arccosine is the angle whose cosine is the specified number. The resulting angle is given in radians in the range zero to pi. | ACOS(0.5)=1.0471975511966 |
| ACOSH | Returns the inverse hyperbolic cosine of a number. The number must be greater than or equal to 1. The inverse hyperbolic cosine is a value whose hyperbolic cosine is a number, so ACOSH(COSH(number)) equals the number. | ACOSH(2)=1.3169578969248 |
| ACOT | Returns the value of the arccotangent (inverse cotangent) of the specified number. | ACOT(3.14)=0.30831566219543 |
| ACOTH | Returns the inverse hyperbolic cotangent of the specified number. | ACOTH(3.14)=0.32994497940173 |
| AMORDEGRC | Returns the depreciation for one accounting period. This function is adapted to the French accounting model. If the asset was acquired during the accounting period, the depreciation is calculated on a straight-line basis. The AMORDEGRC function is similar to the AMORLINC function, but differs in that the depreciation coefficient depends on the useful life of the asset. | AMORDEGRC(2400, 39679, 39813, 300, 1, 0.15, 1)=776 |
| AMORLINC | Returns the depreciation for one accounting period. This function is adapted to the French accounting model. If the asset was acquired during the accounting period, proportional depreciation is considered. | AMORLINC(2400, 39679, 39813, 300, 1, 0.15, 1)=360 |
| ARABIC | Converts Roman numerals to Arabic numerals. | ARABIC(V)=5 |
| ASIN | Returns the arcsine (the inverse of the sine) of the specified number. The arcsine is the angle whose sine is the specified number. The resulting angle is given in radians in the interval from pi/2 to pi/2. | ASIN(1)=1.5707963267949 |
| ASINH | Returns the hyperbolic arcsine of the specified number. The hyperbolic arcsine is a value whose hyperbolic sine is the specified number, so ARCSINH(SINH(number)) is equal to the specified number. | ASINH(1)=0.88137358701954 |
| ATAN | Returns the arctangent (the inverse of the tangent function) of the specified number. The arctangent is the angle whose tangent is the specified number. The resulting angle is given in radians in the range pi/2 to pi/2. | ATAN(2)=1.1071487177941 |
| ATAN2 | Returns the arctangent (the inverse of tangent) of the specified x and y coordinates. The arctangent is the angle between the x axis and the line containing the origin (0;0) and the point at coordinates (x_number, y_number). This angle is given in radians in the interval -pi to pi, except for the value -pi. | ATAN2(2, 3)=0.98279372324733 |
| ATANH | Returns the arctangent (the inverse of the tangent function) of the specified number. The arctangent is the angle whose tangent is the specified number. The resulting angle is given in radians in the range pi/2 to pi/2. | ATANH(0.5)=0.54930614433405 |
| AVEDEV | Returns the average of the absolute deviations of data points from their mean. STANDARD DEVIATION is a measure of the variability of a data set. | AVEDEV(10, 30, 2, 3)=9.375 |
| AVERAGEA | Calculates the average (arithmetic mean) of the values in the argument list. | AVERAGEA(10, 20, 30)=20 |
| BESSELI | Returns a modified Bessel function that is equivalent to the Bessel function calculated for purely imaginary arguments. | BESSELI(1, 2)=0.1357476665807 |
| BESSELJ | Returns the Bessel function. | BESSELJ(1, 2)=0.1149034849319 |
| BESSELK | Returns a modified Bessel function that is equivalent to the Bessel function calculated for purely imaginary arguments. | BESSELK(1, 2)=1.6248388844172 |
| BESSELY | Returns the Bessel function, also known as the Weber or Neumann function. | BESSELY(1, 2)=-1.6506826133039 |
| BIN2DEC | Converts a binary number to decimal. | BIN2DEC(1101)=13 |
| CEILING | Rounds a number up to the nearest integer or to the nearest multiple of significance. | CEILING(1.2)=2 |
| CEILING.MATH | The CEILING.MATH function rounds a number up to the nearest integer or, optionally, to the nearest multiple of significance. | CEILING.MATH(1.2, 1)=2 |
| CEILING.PRECISE | Returns a number that is rounded up to the nearest integer or to the nearest multiple of significance. Regardless of the sign of the number, the number is rounded up. However, if the number or the significance is zero, zero is returned. | CEILING.PRECISE(1.2, 1)=2 |
| CHIDIST | Returns the right-tailed probability of a chi-square distribution. The χ2 distribution is related to the χ2 test. The χ2 test compares observed and expected values. For example, in a genetic experiment, you might predict that the next generation of plants will have flowers of a certain color. By comparing the observed results with the expected results, you can determine whether the original prediction is valid. | CHIDIST(15, 15)=0.45141721122575 |
| CHIINV | Returns the inverse of the right-tailed probability distribution function of the chi-square distribution. If the probability is equal to CHIDIST(x;...), the value of CHIINV(probability;...) is equal to x. Use this function to compare observed results with expected results to determine whether the original assumption is valid. | CHIINV(0.05, 10)=18.307038053334 |
| CODE | Returns the numeric code of the first character of a given text string. | CODE(1)=49 |
| COMBIN | Returns the number of combinations for a specified number of elements. Use the COMBIN function to determine the total number of possible groups for a specified number of elements. | COMBIN(15, 9)=5005 |
| COMBINA | Returns the number of combinations (with repetition) for a given number of items. | COMBINA(15, 6)=38760 |
| COS | Returns the cosine of the specified angle. | COS(1)=0.54030230586814 |
| COSH | Returns the hyperbolic cosine of the specified number. | COSH(1)=1.5430806348152 |
| COT | Returns the cotangent of an angle specified in radians. | COT(1)=0.64209261593433 |
| COTH | Returns the hyperbolic cotangent of a hyperbolic angle. | COTH(1)=1.3130352854993 |
| COUNT | Returns the number of items in the argument list. | COUNT(1, 2)=2 |
| CSC | Returns the cosecant of an angle specified in radians. | CSC(1)=1.1883951057781 |
| CSCH | Returns the hyperbolic cosecant of an angle specified in radians. | CSCH(1)=0.85091812823932 |
| DEGREES | Converts radians to degrees. | DEGREES(PI())=180 |
| DELTA | Tests the equality of two numbers. Returns 1 if number1 = number2; otherwise, returns 0. This function can be used to filter a set of values. For example, when adding several DELTA functions, you can find the number of identical pairs. This function is also known as the Kronecker Delta function. | DELTA(2, 2)=1 |
| DEVSQ | Returns the sum of the squares of the deviations of data points from their sample mean. | DEVSQ(10, 3, 2)=38 |
| EXP | Returns e raised to the power of the argument number. The constant e is equal to 2.718281828459, the base of natural logarithms. | EXP(1)=2.718281828459 |
| FACT | Returns the factorial of a number. The factorial of a number is equal to 1*2*3*...* number. | FACT(9.5)=362880 |
| FACTDOUBLE | Returns the double factorial of the specified number. | FACTDOUBLE(12)=46080 |
| FISHER | Returns the Fisher transformation value of x. This transformation produces a function with a normal distribution rather than a skewed distribution. You can use this function to test the hypothesis about the correlation coefficient. | FISHER(0.9)=1.4722194895832 |
| FISHERINV | Returns the inverse of the Fisher transform. You can use this transform to analyze correlations between regions or matrices of data. If y = FISHER(x), FISHERINV(y) = x. | FISHERINV(10)=0.99999999587769 |
| FLOOR | Rounds a number down to the nearest whole number or to the nearest multiple of the specified value. | FLOOR(1.2)=1 |
| GAMMA | Returns the value of the gamma function. | GAMMA(12)=39916800.000056 |
| GAMMALN | Returns the natural logarithm of the gamma function. | GAMMALN(12)=17.502307845875 |
| GAUSS | Calculates the probability that a member of a standard population falls within the interval between the mean standard deviation and the standard deviation z from the mean. | GAUSS(12)=0.5 |
| GCD | Returns the greatest common divisor of two or more integers. | GCD(12, 15, 1.5)=1 |
| GEOMEAN | Returns the geometric mean of an array or range of positive data. For example, you can use the GEOMEAN function to calculate the average growth rate of a given compound interest with a variable interest rate. | GEOMEAN(5, 2)=3.1622776601684 |
| GESTEP | It returns a value of 1 if the number ≥ the specified value, otherwise it returns 0 (zero). | GESTEP(5, 2)=1 |
| HARMEAN | Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. | HARMEAN(10, 3)=4.6153846153846 |
| INDEX | Returns the value of the element in the array at the selected index. | INDEX((15, 20), 1)=15 |
| INT | Rounds a number down to the nearest integer. | INT(1.2)=1 |
| LCM | Returns the least common multiple of integers. The least common multiple is the smallest positive integer that is a multiple of all integer arguments number1, number2, and so on. Use LCM to add fractions with different denominators. | LCM(10, 6, 3)=30 |
| LN | Returns the natural logarithm of a number. The base of the natural logarithm is the constant e (2.71828182845904). | LN(10)=2.302585092994 |
| LOG | Returns the logarithm of a number to a given base. | LOG(10, 3)=2.0959032742894 |
| LOG10 | Returns the base 10 logarithm of a number. | LOG10(10)=1 |
| MAX | Returns the maximum value in a set of values. | MAX(10, -10)=10 |
| MAXA | Returns the maximum value in a set of values. | MAXA(10, -10, TRUE)=10 |
| MEDIAN | Returns the median of the specified numbers. The median is the number that lies in the middle of a set of numbers. | MEDIAN(10, 20, 15, 1)=12.5 |
| MIN | Returns the minimum value in a set of values. | MIN(10, -10)=-10 |
| MOD | Returns the remainder after dividing a number by a divisor. | MOD(20, 3)=2 |
| MODE | Returns the most frequently occurring or recurring value in a range of data. | MODE(20, 3, 20, 3, 26, 3)=3 |
| MROUND | Returns a number rounded to the desired multiple. | MROUND(20, 2)=20 |
| MULTINOMIAL | Returns the factorial of the sum of values divided by the product of their factorials. | MULTINOMIAL(10, 20, 30)=3.553261127085E+24 |
| PERMUT | Returns the number of permutations for a given number of objects that can be selected from number objects. A permutation is any set or subset of objects or events where internal order is significant. Permutations are different from combinations, for which the internal order is not significant. Use this function for lottery-style probability calculations. | PERMUT(10, 2)=90 |
| PERMUTATIONA | Returns the number of permutations for a given number of objects (with repetitions) that can be selected from the total objects. | PERMUTATIONA(10, 2)=100 |
| PHI | Returns the value of the density function for the standard deviation. | PHI(2)=0.053990966513188 |
| PI | Returns the number 3.1415926535898, the mathematical constant pi. | PI()=3.1415926535898 |
| POWER | Returns the power of a number. | POWER(3, 2)=9 |
| QUOTIENT | Returns the whole part of a division. This function is used to remove the remainder after division. | QUOTIENT(3, 2)=1 |
| RADIANS | Converts degrees to radians. | RADIANS(180)=3.1415926535898 |
| RAND | RAND returns uniformly distributed random real numbers greater than or equal to 0 and less than 1. A new random real number is returned each time the worksheet is recalculated. | RAND()=0.78712665512558 |
| RANDBETWEEN | Returns a random integer from the specified interval. A new random integer is returned each time the worksheet is recalculated. | RANDBETWEEN(180, 220)=202 |
| ROUNDDOWN | Rounds a number down towards zero. | ROUNDDOWN(180.66669, 3)=180.666 |
| ROUNDUP | Rounds a number up, away from zero. | ROUNDUP(180.66669, 3)=180.667 |
| SEC | Returns the secant of an angle. | SEC(0.5)=1.1394939273245 |
| SECH | Returns the hyperbolic secant of an angle. | SECH(1)=0.64805427366389 |
| SIGN | Returns the sign of the argument. Returns 1 if the number is positive, 0 for 0, and -1 if the number is negative. | SIGN(1)=1 |
| SIN | Returns the sine of a given angle. | SIN(PI()/6)=0.5 |
| SINH | Returns the hyperbolic sine of a number. | SINH(PI()/6)=0.54785347388804 |
| SKEW | Returns the skewness of the distribution of a random variable. Skewness indicates the degree of asymmetry of the distribution of the variable around the mean. Positive skewness indicates a distribution with an asymmetric side that is skewed toward more positive values. Negative skewness indicates a distribution with an asymmetric side that is skewed toward more negative values. | SKEW(10, 3, 4, 5)=1.5970779829308 |
| SKEW.P | Returns the skewness coefficient of a distribution based on a set of values: a characteristic of the degree of skewness of the distribution around the mean value. | SKEW.P(12, 5, 6)=0.65201211704405 |
| SMALL | Returns the kth smallest value in a data set. This function is used to determine the value that has a specific relative position in a data set. | SMALL((12, 15), 2)=15 |
| SQRT | Returns the positive square root. | SQRT(100)=10 |
| STDEVP | Calculates standard deviation based on the entire population given as arguments. The standard deviation is a measure of how widely values are dispersed from the average value (the mean). | STDEVP(10, 20)=5 |
| SUM | Returns the sum of all numbers. | SUM(-2, 20)=18 |
| TAN | Returns the tangent of the specified angle. | TAN(1)=1.5574077246549 |
| TANH | Returns the hyperbolic tangent of the argument. | TANH(1)=0.76159415595576 |
- The symbol indicates a web page with an with calculation or data.
- The symbol indicates a web page with an with information for the given issue (it is the default page).
- The symbol indicates a web page with an list of symbol.
- The symbol indicates a web page with an image.
- The symbol indicates a web page with an unit converters.
- The symbol indicates a web page with an RAL colors.
- The symbol indicates a web page with an icon.
- The symbol indicates a web page with an basic equations.
f_x - The symbol indicates a web page with functions.
- The symbol indicates a web page with an with information for users.
Basic - (example: Hydraulic engineering) searches for the entered expression in an exact match with the entry - i.e. in the order in which the words follow each other.
Logical OR - (example: butterfly valve OR lattice disc) pages containing one, the other, or both of the entered keywords will be included in the results.
Logical AND - (example: ASME AND internal pressure) only pages containing both required words will appear in the results.
Logical NOT - (example: spherical NOT ASME) pages containing the name "spherical" but not containing the word "ASME" will be displayed in the results.
\text{if }\ \text{Region}= 2γ^o_{πτ}=0\text{else if }\ \text{Region}= 5γ^o_{πτ}=0\text{else}γ^o_{πτ}=0