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Article Dans Une Revue Ramanujan Journal Année : 2012

The evaluation of a quartic integral via Schwinger, Schur and Bessel

T. Amdeberhan
  • Fonction : Auteur
V. H. Moll
  • Fonction : Auteur
Christophe Vignat

Résumé

We provide additional methods for the evaluation of the integral N-0,N-4(a; m) := integral(infinity)(0) dx/(x(4) + 2ax(2) + 1)(m+1), where m is an element of N and a is an element of (-1, infinity) in the form N-0,N-4(a; m) = pi/2(m+ 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.

Dates et versions

hal-00831855 , version 1 (07-06-2013)

Identifiants

Citer

T. Amdeberhan, V. H. Moll, Christophe Vignat. The evaluation of a quartic integral via Schwinger, Schur and Bessel. Ramanujan Journal, 2012, 28 (1), pp.1-14. ⟨10.1007/s11139-010-9291-9⟩. ⟨hal-00831855⟩
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