Special Functions

  • Victor Barcilon


This chapter on special functions is not meant as a substitute for the handbooks devoted to this subject. Rather, it constitutes an attempt to collect some of the most frequently used formulas involving special functions and to provide a thread for the reader interested in unifying what may seem to be disconnected results.


Asymptotic Expansion Special Function Integral Representation Entire Function Piecewise Smooth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 7-1.
    Abramowitz, M., and Stegun, I. A., (editors), Handbook of Mathematical Functions, National Bureau of Standards, Wash., D.C., 1964.Google Scholar
  2. 7-2.
    Erdélyi, A., et al., Higher Transcendental Functions, 3 vols., McGraw-Hill, New York, 1953.Google Scholar
  3. 7-3.
    Whittaker, E. T., and Watson, G. N., A Course of Modern Analysis, Fourth Edition, Cambridge University Press, Cambridge, 1952.Google Scholar
  4. 7-4.
    Boas, R. P., Jr., Entire Functions, Academic Press, New York, 1954.Google Scholar
  5. 7-5.
    Muller, C., Spherical Harmonics, Springer-Verlag, New York, 1966.Google Scholar
  6. 7-6.
    Buchholz, H., The Confluent Hypergeometric Function, Springer-Verlag, New York, 1969.Google Scholar
  7. 7-7.
    -7 Slepian, D., and Pollak, H. O., “Prolate Spheroidal Wave Functions. Fourier Analysis and Uncertainty—I,” Bell System Technical Journal, 40, 43–64, 1962.Google Scholar


  1. McBride, E., Obtaining Generating Functions, Springer-Verlag, New York, 1971.Google Scholar
  2. Miller, W., Lie Theory and Special Functions, Academic Press, New York, 1968.Google Scholar
  3. Truesdell, C, C., “An Essay Toward a Unified Theory of Special Functions,” Annals of Mathematical Studies, Princeton University Press, Princeton, 1948.Google Scholar

Copyright information

© Van Nostrand Reinhold 1990

Authors and Affiliations

  • Victor Barcilon
    • 1
  1. 1.Dep’t. of the Geophysical SciencesUniversity of ChicagoChicagoUSA

Personalised recommendations