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 [https://en.wikipedia.org/wiki/Beta capital $\beta$] in Greek) is defined by the following formula for $\mathrm{Re}(x)>0$ and $\mathrm{Re}(y)>0$: |
$$B(x,y)=\displaystyle\int_0^1 t^{x-1}(1-t)^{y-1} \mathrm{d}t.$$ | $$B(x,y)=\displaystyle\int_0^1 t^{x-1}(1-t)^{y-1} \mathrm{d}t.$$ | ||
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=References= | =References= | ||
| − | + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=findme|next=findme}}: $\S 1.5 (1)$ | |
| − | |||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 15:34, 23 June 2016
The beta function $B$ (note: $B$ is capital $\beta$ in Greek) is defined by the following formula for $\mathrm{Re}(x)>0$ and $\mathrm{Re}(y)>0$: $$B(x,y)=\displaystyle\int_0^1 t^{x-1}(1-t)^{y-1} \mathrm{d}t.$$
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
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.5 (1)$
