# Ојлеров интеграл

У математици, постоје два типа Ојлеровог интеграла:

1. Ојлеров интеграл прве врсте: Бета-функција
${\displaystyle \mathrm {B} (x,y)=\int _{0}^{1}t^{x-1}(1-t)^{y-1}\,dt={\frac {\Gamma (x)\Gamma (y)}{\Gamma (x+y)}}}$
2. Ојлеров интеграл друге врсте: Гама-функција
${\displaystyle \Gamma (z)=\int _{0}^{\infty }t^{z-1}\,e^{-t}\,dt}$

За позитивне цијеле бројеве m и n

${\displaystyle \mathrm {B} (n,m)={(n-1)!(m-1)! \over (n+m-1)!}={n+m \over nm{n+m \choose n}}}$
${\displaystyle \Gamma (n)=(n-1)!\,}$

## Литература

• Milton Abramowitz and Irene Stegun, editors. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.
• I.S. Gradshteyn; I.M. Ryzhik; Alan Jeffrey; Daniel Zwillinger (2007). Table of Integrals, Series, and Products (7th изд.). Academic Press. ISBN 978-0-12-373637-6.
• A.P. Prudnikov (А. П. Прудников), Yu.A. Brychkov (Ю. А. Брычков), O.I. Marichev (О. И. Маричев). Integrals and Series. First edition (Russian), volume 1–5, Nauka, 1981−1986. First edition (English, translated from the Russian by N.M. Queen), volume 1–5, Gordon & Breach Science Publishers/CRC Press, 1988–1992. ISBN 2-88124-097-6.. Second revised edition (Russian), volume 1–3, Fiziko-Matematicheskaya Literatura, 2003.
• Yu.A. Brychkov (Ю. А. Брычков). Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas. Russian edition, Fiziko-Matematicheskaya Literatura, 2006. English edition, Chapman & Hall/CRC Press. 2008. ISBN 1-58488-956-X
• Zwillinger, Daniel (2002). CRC Standard Mathematical Tables and Formulae (31stlocation= изд.). Chapman & Hall/CRC Press. ISBN 1-58488-291-3.'
• Meyer Hirsch, Integral Tables, Or, A Collection of Integral Formulae (Baynes and son, London, 1823) [English translation of Integraltafeln]
• Peirce, Benjamin Osgood (1800). A Short Table of Integrals. Ginn.