Manuals/calci/BETAFUNCTION

BETAFUNCTION (a,b)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} are any positive real numbers.

Description

• This function returns the value of the Beta function.
• Beta function is also called the Euler integral of the first kind.
• To evaluate the Beta function we usually use the Gamma function.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(x,y)=\frac{Gamma(x)Gamma(y)}{Gamma(x+y)}} .

• For x,y positive we define the Beta function by:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(x,y)= \int\limits_{0}^{1} t^{x-1}(1-t)^{y-1} dt}