These integrals turn up in subjects such as quantum field theory. A few important definite integrals involving ex2 e x 2 have pleasant closed form. By elementary function we mean something obtained using arithmetical operations and composition from the standard functions we all know and love. The n + p = 0 mod 2 requirement is because the integral from −∞ to 0 contributes a factor of (−1) n+ p/2 to each term, while the integral from 0 to +∞ contributes a factor of 1/2 to each term. 14 There is no elementary function whose derivative is ex2 e x 2.
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