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Bessel functions

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Formulas and Theorems for the Special Functions of Mathematical Physics

Part of the book series: Die Grundlehren der mathematischen Wissenschaften ((GL,volume 52))

Abstract

Bessel functions are solutions of Bessel’s differential equation

$${z^2}\frac{{{d^2}w}}{{d{z^2}}} + z\frac{{dw}}{{dz}} + ({z^2} - {v^2})w = 0,{\text{ }}v,z{\text{can be arbitrarily complex}}$$

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Literature

  • Erdélyi, A.: Higher transcendental functions, vol. 2. New York: McGraw-Hill 1953.

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  • Gray, A., G. B. Mathews and T. M. MacRobert: A treatise on the theory of Bessel functions. London: Macmillan 1931.

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  • McLachlan, N. W.: Bessel functions for Engineers. Oxford: Clarendon press 1955.

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  • Petiau, G.: La theorie des fonctions de Bessel. Paris 1955.

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  • Watson, G. N.: A treatise on the theory of Bessel functions. Cambridge: U. Press 1952.

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  • Wetrich, R.: Die Zylinderfunktionen und ihre Anwendungen. Leipzig: Teubner 1937.

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Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, USA

    Dr. Wilhelm Magnus (Professor)

  2. Oregon State University, USA

    Dr. Fritz Oberhettinger (Professor)

  3. International Business Machines Corporation, USA

    Dr. Raj Pal Soni (Mathematician)

Authors
  1. Dr. Wilhelm Magnus
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  2. Dr. Fritz Oberhettinger
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  3. Dr. Raj Pal Soni
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© 1966 Springer-Verlag Berlin Heidelberg

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Magnus, W., Oberhettinger, F., Soni, R.P. (1966). Bessel functions. In: Formulas and Theorems for the Special Functions of Mathematical Physics. Die Grundlehren der mathematischen Wissenschaften, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11761-3_3

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  • DOI: https://doi.org/10.1007/978-3-662-11761-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-11763-7

  • Online ISBN: 978-3-662-11761-3

  • eBook Packages: Springer Book Archive

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