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Transactions of the American Mathematical Society

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Neumann series of Bessel functions


Author: J. Ernest Wilkins
Journal: Trans. Amer. Math. Soc. 64 (1948), 359-385
MSC: Primary 42.4X
DOI: https://doi.org/10.1090/S0002-9947-1948-0027092-X
MathSciNet review: 0027092
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    H. Bateman, On an expansion of an arbitrary function in a series of Bessel functions, Messenger of Mathematics vol. 36 (1907) pp. 31-37. A. Gray, G. B. Mathews, and T. M. MacRobert, A treatise on Bessel functions, MacMillan, 1931. W. Kapteyn, On a series of Bessel functions, Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings of the Section of Sciences, vol. 7 (1905) pp. 494-500. ---, On an expansion of an arbitrary function in a series of Bessel functions, Messenger of Mathematics vol. 35 (1906) pp. 122-125. W. V. Lovitt, Linear integral equations, McGraw-Hill, 1924. S. Pincherle, Sopra alcuni sviluppi in serie per funzioni analitiche, R. Accademia delle scienze dell’Istituto di Bologna, Memoria (4) vol. 3 (1881) pp. 151-180. E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford University Press, 1939. ---, The theory of functions, Oxford University Press, 1939.
  • G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
  • H. A. Webb, The expansion of an arbitrary function in a series of Bessel functions, Messenger of Mathematics vol. 33 (1904) pp. 55-58. E. T. Whittaker and G. N. Watson, Modern analysis, Cambridge University Press, 1943.

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Article copyright: © Copyright 1948 American Mathematical Society