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Bulletin of the American Mathematical Society

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Book Review

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Book Information:

Author: Harry Hochstadt
Title: The functions of mathematical physics
Additional book information: Pure and Applied Mathematics, Vol. 23, Wiley-Interscience, New York, 1971, xi+322 pp., $17.50.

References [Enhancements On Off] (What's this?)

  • 1. E. Cartan, Sur la determination d'un systeme orthogonal complet dans un espace Riemann symmetrique clos, Rend. Cire. Mat. Palermo 53 (1929), 217-252.
  • 2. A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions. Vols. 1-3, McGraw-Hill, New York, 1953, 1955. MR 15,419; 16,586.
  • 3. Géza Freud, Orthogonale Polynome, Birkhäuser Verlag, Basel-Stuttgart, 1969 (German). Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften, Mathematische Reihe, Band 33. MR 0481888
  • 4. Harry Hochstadt, Special functions of mathematical physics, Athena Series: Selected Topics in Mathematics, Holt, Rinehart and Winston, New York, 1961. MR 0153137
  • 5. E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Chelsea Publishing Company, New York, 1955. MR 0064922
  • 6. N. N. Lebedev, Special functions and their applications, Revised English edition. Translated and edited by Richard A. Silverman, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0174795
  • 7. Y. L. Luke, The special functions and their approximations. Vols. 1, 2, Math. in Sci. and Engineering, vol. 53, Academic Press, New York, 1969. MR 39 #3039; 40 #2909.
  • 8. Thomas M. Macrobert, Functions of a Complex Variable, Macmillan and Co., Limited, London, 1947. 3d ed. MR 0021087
  • 9. T. M. MacRobert, Spherical harmonics. An elementary treatise on harmonic functions with applications, Third edition revised with the assistance of I. N. Sneddon. International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford-New York-Toronto, Ont., 1967. MR 0220985
  • 10. Elna B. McBride, Obtaining generating functions, Springer Tracts in Natural Philosophy, Vol. 21, Springer-Verlag, New York-Heidelberg, 1971. MR 0279355
  • 11. Willard Miller Jr., Lie theory and special functions, Mathematics in Science and Engineering, Vol. 43, Academic Press, New York-London, 1968. MR 0264140
  • 12. F. W. J. Olver, Asymptotics and special functions, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Computer Science and Applied Mathematics. MR 0435697
  • 13. Earl D. Rainville, Special functions, The Macmillan Co., New York, 1960. MR 0107725
  • 14. G. Sansone, Orthogonal functions, Revised English ed. Translated from the Italian by A. H. Diamond; with a foreword by E. Hille. Pure and Applied Mathematics, Vol. IX, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1959. MR 0103368
  • 15. Ian N. Sneddon, Special functions of mathematical physics and chemistry, Oliver and Boyd, Edinburgh and London; Intersciences Publishers, Inc., New York, 1956. MR 0080170
  • 16. B. Spain and M. G. Smith, Functions of mathematical physics, Van Nostrand Rheinhold, London, 1970.
  • 17. Gábor Szegő, Orthogonal polynomials, 3rd ed., American Mathematical Society, Providence, R.I., 1967. American Mathematical Society Colloquium Publications, Vol. 23. MR 0310533
  • 18. James D. Talman, Special functions: A group theoretic approach, Based on lectures by Eugene P. Wigner. With an introduction by Eugene P. Wigner, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0239154
  • 19. C. A. Truesdell, An essay toward a unified theory of special functions based upon the functional equation (∂/∂z)F(z,α) = F(z,α + 1), Ann. of Math. Studies, no. 18, Princeton Univ. Press, Princeton, N.J., 1948. MR 9, 431.
  • 20. N. Ja. Vilenkin, Special functions associated with class 1 representations of the motion groups of spaces of constant curvature, Trudy Moskov. Mat. Obšč. 12 (1963), 185–257 (Russian). MR 0162887
  • 21. N. Ja. Vilenkin, \cyr Spetsial′nye funktsii i teoriya predstavleniĭ grupp, Izdat. “Nauka”, Moscow, 1965 (Russian). MR 0209523
  • 22. G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
  • 23. E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469

Review Information:

Reviewer: Ian N. Sneddon
Journal: Bull. Amer. Math. Soc. 82 (1976), 237-243