Elliptic integrals, theta functions and elliptic functions

Magnus, Wilhelm; Oberhettinger, Fritz; Soni, Raj Pal

doi:10.1007/978-3-662-11761-3_10

Wilhelm Magnus⁶,
Fritz Oberhettinger⁷ &
Raj Pal Soni⁸

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

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Abstract

General remarks. Any integral of the type ∫ R \(\left( {z,{Z^{\frac{1}{2}}}} \right)\) is a rational function of x and y and Z is a polynomial of the third or fourth degree in z with real coefficients and no repeated factors is called an elliptic integral.

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Literature

Bellman, R.: A brief introduction to theta functions. New York: Holt, Rinehart and Winston 1961.
MATH Google Scholar
Byrd, P., and M. Friedman: Handbook of elliptic integrals for engineers and physicists. Berlin/Göttingen/Heidelberg: Springer 1954.
MATH Google Scholar
Erdélyi, A.: Higher transcendental functions, Vol. 2. New York: Mc-Graw-Hill 1953.
Google Scholar
Hancock, H.: Theory of elliptic functions. New York: Dover 1958.
MATH Google Scholar
Hancock, H.: Elliptic integrals. New York: Wiley 1917.
Google Scholar
Jahnke, E., F. Emde and F. Loesch: Tables of higher functions. New York: McGraw-Hill 1960.
MATH Google Scholar
Milne-Thomson, L. M.: Jacobian elliptic function tables. New York: Dover 1950.
MATH Google Scholar
MacRobert, T. M.: Functions of a complex variable. London: MacMillan 1958.
Google Scholar
Neville, E. H.: Jacobian elliptic functions. Oxford 1951.
Google Scholar
Oberhettinger, F., and W. Magnus: Anwendung der elliptischen Funktionen in Physik und Technik. Berlin/Göttingen/Heidelberg: Springer 1949.
Book MATH Google Scholar
Schuler, M., und H. Gebelein: Five place tables of elliptic functions. Berlin/Göttingen/Heidelberg: Springer 1955.
Book Google Scholar
Tricomi, F.: Elliptische Funktionen. Berlin/Göttingen/Heidelberg: Springer 1948.
MATH Google Scholar
Whittaker, E. T., and G. N. Watson: A course of modern analysis. Cambridge 1944.
Google Scholar

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Authors and Affiliations

Courant Institute of Mathematical Sciences, New York University, USA
Dr. Wilhelm Magnus (Professor)
Oregon State University, USA
Dr. Fritz Oberhettinger (Professor)
International Business Machines Corporation, USA
Dr. Raj Pal Soni (Mathematician)

Authors

Dr. Wilhelm Magnus
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Dr. Fritz Oberhettinger
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Dr. Raj Pal Soni
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Magnus, W., Oberhettinger, F., Soni, R.P. (1966). Elliptic integrals, theta functions and elliptic 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_10

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DOI: https://doi.org/10.1007/978-3-662-11761-3_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-11763-7
Online ISBN: 978-3-662-11761-3
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