beta( z , w )

The beta function of z and w in SageMath. Defined by

\[ \operatorname{B} (z,w) = \int_0^1 dt \; t^{z-1} (1-t)^{w-1} \]

Relation to gamma:

\[ \operatorname{B} (z,w) = \frac{ \Gamma(z) \Gamma(w) }{ \Gamma(z+w) } \]

Plot on the real axis:

Series expansions about unity:

Special values:

Related functions:   binomial   gamma

Function category: gamma functions sagemath-docs