Eulerov integral

U matematici, postoje dva tipa Eulerovog integrala:^[1]

1. Eulerov integral prvog reda: tzv. Beta funkcija

B (x, y) = \int_{0}^{1} t^{x - 1} (1 - t)^{y - 1} d t = \frac{Γ (x) Γ (y)}{Γ (x + y)}

2. Eulerov integral drugog reda: tzv. Gama funkcija

Γ (z) = \int_{0}^{\infty} t^{z - 1} e^{- t} d t

B (n, m) = \frac{(n - 1)! (m - 1)!}{(n + m - 1)!} = \frac{n + m}{n m (\binom{n + m}{n})}

Γ (n) = (n - 1)!

Također pogledajte

Milton Abramowitz and Irene Stegun, editors. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.
I.S. Gradshteyn (И. С. Грaдштейн), I.M. Ryzhik (И. М. Рыжик); Alan Jeffrey, Daniel Zwillinger, editors. Table of Integrals, Series, and Products, seventh edition. Academic Press, 2007. Šablon:ISBN. Errata. (Several previous editions as well.)
A.P. Prudnikov (А. П. Прудников), Yu.A. Brychkov (Ю. А. Брычков), O.I. Marichev (О. И. Мaричев). 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, Šablon:ISBN. 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, Šablon:ISBN.
Daniel Zwillinger. CRC Standard Mathematical Tables and Formulae, 31st edition. Chapman & Hall/CRC Press, 2002. Šablon:ISBN. (Many earlier editions as well.)
Meyer Hirsch, Integral Tables, Or, A Collection of Integral Formulae (Baynes and son, London, 1823) [English translation of Integraltafeln]
Benjamin O. Pierce A short table of integrals - revised edition (Ginn & co., Boston, 1899)

↑ Jeffrey, Alan; and Dai, Hui-Hui (2008). Handbook of Mathematical Formulas 4th Ed. Academic Press. Šablon:ISBN. str. 234-235