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The H-function associated with a certain class of Feynman integrals. (English) Zbl 0695.33002
Motivated by some further examples of the use of Feynman integrals which arise in perturbation calculus of the equilibrium properties of a magnetic model of phase transitions, a generlization of the familiar H- function of Ch. Fox [Trans. Am. Math. Soc. 98, 395-429 (1961; Zbl 0096.308)] was proposed recently by A. A. Inayat-Hussain [J. Phys. A 20, 4109-4117 and 4119-4128 (1987; Zbl 0634.33005 and Zbl 0634.33006)]. A brief discussion of contour selection and convergence conditions at the integrals involved is presented. It is also shown how some recent work of the first author [Jñānābha, Sect. A 2, 39-47 (1972; Zbl 0289.33012); Indian J. Pure Appl. Math. 18, 536-547 (1987; Zbl 0632.33004); Indian J. Math. 32, 25-32 (1990)] can be applied to derive various recurrence relations for the general \(\bar H-\)function. Finally some relevant comments are made on the validity and novelty of two summation formulas for the Clausenian hypergeometric function, which were derived by Inayat-Hussain.

MSC:
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
33C20 Generalized hypergeometric series, \({}_pF_q\)
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