Elliptic integrals, theta functions and elliptic functions

  • Wilhelm Magnus
  • Fritz Oberhettinger
  • Raj Pal Soni
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 52)


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

Copyright information

© Springer-Verlag Berlin Heidelberg 1966

Authors and Affiliations

  • Wilhelm Magnus
    • 1
  • Fritz Oberhettinger
    • 2
  • Raj Pal Soni
    • 3
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityUSA
  2. 2.Oregon State UniversityUSA
  3. 3.International Business Machines CorporationUSA

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