Table of integrals: Difference between revisions

Revision as of 23:08, 6 October 2006

Revision as of 23:13, 6 October 2006

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:<math>\int_0^\infty x^{z-1}\,e^{-x}\,dx = \Gamma(z)</math> (where <math>\Gamma(z)</math> is the [[Gamma function]])

:<math>\int_{-\infty}^\infty \exp\left[-(ax^2+bx+c)\right]\,dx=\sqrt{\frac{\pi}{a}}\exp\left[\frac{b^2-4ac}{4a}\right]</math> (where <math> \exp\left[u\right]</math> =is the [[exponential function]] <math> e^u </math>.)

:<math>\int_{0}^{2 \pi} e^{x \cos \theta} d \theta = 2 \pi I_{0}(x)</math> (where <math>I_{0}(x)</math> is the modified [[Bessel function]] of the first kind)