2010/09/13 by Tewodros Amdeberhan, Amdeberhan, Tewodros, Victor H. Moll +2
Mathematics · #Algebraic and Geometric Analysis #Mathematical functions and polynomials #Mathematics and Applications
paper · doi:10.48550/arxiv.1009.2399
We provide additional methods for the evaluation of the integral N0,4(a;m) amp; := amp; ∫0∞ \fracdx ( x4 + 2ax2 + 1 )m+1 where m ∈ ℕ and a ∈ (-1, ∞) in the form N0,4(a;m) amp; = amp; \fracπ2m+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.