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