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}

Examples

1. BETAFUNCTION(10,23) = 1.550093439705759e-9
2. BETAFUNCTION(9.1,7.4) = 0.00001484129272494359
3. BETAFUNCTION(876,432) = NaN

See Also

• BETADISTX
• BETAINV

References

Beta Function

• List of Main Z Functions

• Z3 home