function complete - meaning and definition. What is function complete
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  3. function complete

What (who) is function complete - definition

MATHEMATICAL FUNCTION
Incomplete beta function; Regularized incomplete Beta function; Regularized Beta function; Incomplete Beta function; Regularized incomplete beta function; Euler beta function; Incomplete beta-function; Complete beta function; Regularized beta function; Beta Function; Β(x, y)
  • Beta function plotted in the complex plane in three dimensions with Mathematica 13.1's ComplexPlot3D
  • [[Contour plot]] of the beta function

function complete      
<programming> State of a software component or system such that each function described by the software's {functional specification} can be reached by at least one {functional path}, and attempts to operate as specified. (1999-04-07)
Functional completeness         
PROPERTY OF A SET OF LOGICAL CONNECTIVES WHICH CAN EXPRESS ALL POSSIBLE TRUTH TABLES BY COMBINING MEMBERS OF THE SET
Complete set of Boolean operators; Sole sufficient operator; Adequacy (logic); Post's functional completeness theorem; Functionally complete; Sufficiently connected; Expressive adequacy; Post's criterion
In logic, a functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression.. ("Complete set of logical connectives")..
https://en.wikipedia.org/wiki/Functional_completeness
Gamma function         
  • [[Daniel Bernoulli]]'s letter to [[Christian Goldbach]], October 6, 1729
  • The first page of Euler's paper
  • The gamma function interpolates the factorial function to non-integer values.
  • reproduction of a famous complex plot by Janhke and Emde (Tables of Functions with Formulas and Curves, 4th ed., Dover, 1945) of the gamma function from -4.5-2.5i to 4.5+2.5i
  • 3-dimensional plot of the absolute value of the complex gamma function
  • </math> is also displayed.
  • Γ(''z'') + sin(π''z'')}} in green. Notice the intersection at positive integers. Both are valid analytic continuations of the factorials to the non-integers.
  • lt=Emde}}.
  • log Γ(''z'')}}
  • Comparison gamma (blue line) with the factorial (blue dots) and Stirling's approximation (red line)
  • Plot of gamma function in complex plane in 3D with color and legend and 1000 plot points created with Mathematica
  • 6+2''i''}} with colors created in Mathematica
  • Plot of logarithmic gamma function in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D
EXTENSION OF THE FACTORIAL FUNCTION, WITH ITS ARGUMENT SHIFTED DOWN BY 1, TO REAL AND COMPLEX NUMBERS
Gamma-function; Complete gamma function; Gamma Function; Gamma integral; Euler Gamma Function; Γ(x); Γ function; Raabe's formula; Approximations of the gamma function; Weierstrass definition of the gamma function; Complex number factorial
In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers.
https://en.wikipedia.org/wiki/Gamma_function

Wikipedia

Beta function

In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral

B ( z 1 , z 2 ) = ∫ 0 1 t z 1 − 1 ( 1 − t ) z 2 − 1 d t {\displaystyle \mathrm {B} (z_{1},z_{2})=\int _{0}^{1}t^{z_{1}-1}(1-t)^{z_{2}-1}\,dt}

for complex number inputs z 1 , z 2 {\displaystyle z_{1},z_{2}} such that ℜ ( z 1 ) , ℜ ( z 2 ) > 0 {\displaystyle \Re (z_{1}),\Re (z_{2})>0} .

The beta function was studied by Leonhard Euler and Adrien-Marie Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital beta.

https://en.wikipedia.org/wiki/Beta function
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