Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Classical analytic representations


Authors: G. L. Curme and Einar Hille
Journal: Quart. Appl. Math. 27 (1969), 185-192
MSC: Primary 30.60
DOI: https://doi.org/10.1090/qam/243074
MathSciNet review: 243074
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Abstract: Mittag-Leffler-like fractional decompositions are constructed for the gamma, Jacobian elliptic and for the quotient of Bessel functions. These results illustrate a technique herein developed which permits a complete ML decomposition of a large class of meromorphic functions without resorting to any other previously derived information or knowledge of the particular function. Typically, the point of departure of this note stands in contrast to a statement in Knopp [1, p. 44], during his development of the ML decomposition of $ \pi \cot \pi z$, which reads as follows: ``The still undetermined entire function, $ G\left( z \right)$, cannot be ascertained solely from the nature and position of the poles."


References [Enhancements On Off] (What's this?)

  • [1] Konrad Knopp, Theory of Functions. II. Applications and Continuation of the General Theory, Dover Publications, New York, 1947. MR 0019722
  • [2] S. Zamoseianyk, Analytic representations of a meromorphic function, Dissertation, Illinois Institute of Technology, 1962
  • [3] N. Nielsen, Handbuch der Theorie der Gammafunction, Leipzig, 1906
  • [4] M. Price, Analytic representations and limit singularities, Dissertation, Illinois Institute of Technology, 1962
  • [5] E. T. Whittaker and G. N. Watson, Modern analysis, Cambridge University Press, 1952
  • [6] G. N. Watson, Theory of Bessel functions, Cambridge University Press, 1963
  • [7] S. F. Musket, Decomposition of quotients of Bessel functions, Dissertation, Illinois Institute of Technology, 1962

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DOI: https://doi.org/10.1090/qam/243074
Article copyright: © Copyright 1969 American Mathematical Society


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