Difference between revisions of "Beta"
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The beta function $B$ (note: $B$ is capital $\beta$ in Greek) is defined by the formula | The beta function $B$ (note: $B$ is capital $\beta$ in Greek) is defined by the formula | ||
| − | $$B(x,y)=\displaystyle\int_0^1 t^{x-1}(1-t)^{y-1} | + | $$B(x,y)=\displaystyle\int_0^1 t^{x-1}(1-t)^{y-1} \mathrm{d}t.$$ |
<div align="center"> | <div align="center"> | ||
Revision as of 05:54, 6 June 2016
The beta function $B$ (note: $B$ is capital $\beta$ in Greek) is defined by the formula $$B(x,y)=\displaystyle\int_0^1 t^{x-1}(1-t)^{y-1} \mathrm{d}t.$$
Properties
Partial derivative of beta function
Beta in terms of gamma
Beta in terms of sine and cosine
Videos
Beta function - Part 1
Beta function
Beta integral function - basic identity
Gamma function - Part 10 - Beta function
Mod-04 Lec-09 Analytic continuation and the gamma function (Part I)
Gamma Function, Transformation of Gamma Function, Beta Function, Transformation of Beta Function
Beta Function - Gamma Function Relation Part 1
Beta Function - Gamma Function Relation Part 2
Beta Integral: Even Powers Of Sine Function
References
Bell. Special Functions
Special functions by Leon Hall
