The Evaluation of a Quartic Integral via Schwinger, Schur and Bessel
نویسندگان
چکیده
0 dx (x4 + 2ax2 + 1) where m ∈ N and a ∈ (−1,∞) in the form N0,4(a;m) = π 2m+3/2(a + 1)m+1/2 Pm(a) where Pm(a) is a polynomial in a. The first one is based on a method of Schwinger to evaluate integrals appearing in Feynman diagrams, the second one is a byproduct of an expression for a rational integral in terms of Schur functions. Finally, the third proof, is obtained from an integral representation involving modified Bessel functions.
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