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Title: Beta Function -- from Wolfram MathWorld

Open Graph Title: Beta Function -- from Wolfram MathWorld

X Title: Beta Function -- from Wolfram MathWorld

Description: The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is defined by B(p,q)=(Gamma(p)Gamma(q))/(Gamma(p+q))=((p-1)!(q-1)!)/((p+q-1)!). (1) The beta function B(a,b) is implemented in the Wolfram Language as Beta[a, b]. To derive the integral representation of the beta function, write the product of two factorials as m!n!=int_0^inftye^(-u)u^mduint_0^inftye^(-v)v^ndv. (2) Now,...

Open Graph Description: The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is defined by B(p,q)=(Gamma(p)Gamma(q))/(Gamma(p+q))=((p-1)!(q-1)!)/((p+q-1)!). (1) The beta function B(a,b) is implemented in the Wolfram Language as Beta[a, b]. To derive the integral representation of the beta function, write the product of two factorials as m!n!=int_0^inftye^(-u)u^mduint_0^inftye^(-v)v^ndv. (2) Now,...

X Description: The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is defined by B(p,q)=(Gamma(p)Gamma(q))/(Gamma(p+q))=((p-1)!(q-1)!)/((p+q-1)!). (1) The beta function B(a,b) is implemented in the Wolfram Language as Beta[a, b]. To derive the integral representation of the beta function, write the product of two factorials as m!n!=int_0^inftye^(-u)u^mduint_0^inftye^(-v)v^ndv. (2) Now,...

Opengraph URL: https://mathworld.wolfram.com/BetaFunction.html

X: @WolframResearch

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Domain: mathworld.wolfram.com

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