The evaluation of a quartic integral via Schwinger, Schur and Bessel
We provide additional methods for the evaluation of the integral where m ∈ℕ and a ∈(−1,∞) in the form where P m ( 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 ratio...
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| Veröffentlicht in: | The Ramanujan journal 2012-05, Vol.28 (1), p.1-14 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We provide additional methods for the evaluation of the integral
where
m
∈ℕ and
a
∈(−1,∞) in the form
where
P
m
(
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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| ISSN: | 1382-4090 1572-9303 |
| DOI: | 10.1007/s11139-010-9291-9 |