Difference between revisions of "Beta"
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[[Beta in terms of sine and cosine]]<br /> | [[Beta in terms of sine and cosine]]<br /> | ||
[[Beta as improper integral]]<br /> | [[Beta as improper integral]]<br /> | ||
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=Videos= | =Videos= | ||
Revision as of 15:37, 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
Beta as improper integral
Beta is symmetric
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): $\S 1.5 (1)$
