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On the evaluation of an integral connected with the thermonuclear reaction rate in closed form
Author(s) -
Haubold H. J.,
John R. W.
Publication year - 1978
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.19782990502
Subject(s) - series (stratigraphy) , thermonuclear fusion , representation (politics) , function (biology) , physics , elementary function , continuation , analytic continuation , integral equation , expression (computer science) , connection (principal bundle) , reaction rate , class (philosophy) , mathematical analysis , mathematics , plasma , quantum mechanics , geometry , computer science , paleontology , evolutionary biology , politics , political science , law , biology , programming language , biochemistry , chemistry , artificial intelligence , catalysis
The standard expression of the reaction rate for low‐energy, nonresonant nuclear reactions in nondegenerate plasma contains a parameter‐dependent integral which in all previous calculations with physical or astrophysical background is considered as not capable of being evaluated in a closed form. So one usually resorts to approximation methods concerning large values of the parameter. At first we point out that C ONSUL (1964) has given a series representation of the integral which was identified with a M EIJER 's G ‐function by M ATHAI (1971). Next, in view of a physically more exact determination of the reaction rate formula, especially in connection with calculations concerning stellar energy generation, we consider a more general integral containing the mentioned one as special case and give an approximation‐free representation by means of M EIJER 's G ‐function. The G ‐function so obtained may be conceived as complex‐valued continuation of C ONSUL 's series representation of a certain class of integrals contained in the considered one. From the series we extract a small parameter approximation of the special integral.