Introduction to Quantum Mechanics (2nd ed.). Weisstein, Eric W.'Gaussian Integral'. The exponential integral EnHzL, exponential integral EiHzL, logarithmic integral li HzL, sine integral Si HzL, hyperbolic sine integral Shi HzL, cosine integral CiHzL, and hyperbolic cosine integral ChiHzL are defined as the following definite integrals, including the Euler gamma constant g0.
'Introduction to integral discriminants'. ^ 'Reference for Multidimensional Gaussian Integral'.^ a b 'The Probability Integral' (PDF).'Integration in Finite Terms with Special Functions: the Error Function'. 'The History of the Normal Distribution' (PDF). These integrals turn up in subjects such as quantum field theory. The n + p = 0 mod 2 requirement is because the integral from â��â�� to 0 contributes a factor of (â�∡) n+ p/2 to each term, while the integral from 0 to +â�� contributes a factor of 1/2 to each term. Since the exponential function is greater than 0 for all real numbers, it then follows that the integral taken over the square's incircle must be less than I(a)2
