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Asymptotics of the hypergeometric function
Author(s) -
Jones D. S.
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.208
Subject(s) - hypergeometric function , lambda , mathematics , function (biology) , generalized hypergeometric function , representation (politics) , confluent hypergeometric function , pure mathematics , hypergeometric distribution , combinatorics , physics , quantum mechanics , evolutionary biology , politics , political science , law , biology
An asymptotic representation is obtained for the hypergeometric function ${\bf F}(a+\lambda,b‐\lambda,c,1/2‐1/2z)$\nopagenumbers\end as $|\lambda|\rightarrow\infty$\nopagenumbers\end with $|{\rm ph}\,\lambda|<\pi$\nopagenumbers\end . It is uniformly valid in the z ‐plane cut in an appropriate way. Several other forms of the hypergeometric function are discussed also. Another representation which has some advantages over the conventional one is given as well. Copyright © 2001 John Wiley & Sons, Ltd.