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mathematical physics > special function > beta function

mathematical analysis > functional analysis > special function > beta function

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beta function

In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral

${\\displaystyle \\mathrm {B} (z_{1},z_{2})=\\int _{0}^{1}t^{z_{1}-1}(1-t)^{z_{2}-1}\\,dt}$

for complex number inputs
${\\displaystyle z_{1},z_{2}}$ such that ${\\displaystyle \\Re (z_{1}),\\Re (z_{2})>0}$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Beta_function)

special function

Euler integral of the first kind

fonction bêta

francés
intégrale d'Euler de première espèce

URI

http://data.loterre.fr/ark:/67375/PSR-J8PV8QXJ-5

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