Book Review
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MathSciNet review:
1566850
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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.
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.
Géza Freud, Orthogonale Polynome, Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften, Mathematische Reihe, Band 33, Birkhäuser Verlag, Basel-Stuttgart, 1969 (German). MR 0481888
Harry Hochstadt, Special functions of mathematical physics, Athena Series: Selected Topics in Mathematics, Holt, Rinehart and Winston, New York, 1961. MR 0153137
E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Chelsea Publishing Co., New York, 1955. MR 0064922
N. N. Lebedev, Special functions and their applications, Revised English edition, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. Translated and edited by Richard A. Silverman. 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.
Thomas M. Macrobert, Functions of a Complex Variable, Macmillan & Co., Ltd., London, 1947. 3d ed. MR 0021087
T. M. MacRobert, Spherical harmonics. An elementary treatise on harmonic functions with applications, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford-New York-Toronto, Ont., 1967. Third edition revised with the assistance of I. N. Sneddon. MR 0220985
Elna B. McBride, Obtaining generating functions, Springer Tracts in Natural Philosophy, Vol. 21, Springer-Verlag, New York-Heidelberg, 1971. MR 0279355
Willard Miller Jr., Lie theory and special functions, Mathematics in Science and Engineering, Vol. 43, Academic Press, New York-London, 1968. MR 0264140
F. W. J. Olver, Asymptotics and special functions, Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. MR 0435697
Earl D. Rainville, Special functions, The Macmillan Company, New York, 1960. MR 0107725
G. Sansone, Orthogonal functions, Pure and Applied Mathematics, Vol. IX, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1959. Revised English ed; Translated from the Italian by A. H. Diamond; with a foreword by E. Hille. MR 0103368
Ian N. Sneddon, Special functions of mathematical physics and chemistry, Oliver and Boyd, Edinburgh-London; Interscience Publishers, Inc., New York, 1956. MR 0080170
16. B. Spain and M. G. Smith, Functions of mathematical physics, Van Nostrand Rheinhold, London, 1970.
Gábor Szegő, Orthogonal polynomials, 3rd ed., American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1967. MR 0310533
James D. Talman, Special functions: A group theoretic approach, W. A. Benjamin, Inc., New York-Amsterdam, 1968. Based on lectures by Eugene P. Wigner; With an introduction by Eugene P. Wigner. 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.
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
N. Ja. Vilenkin, Spetsial′nye funktsii i teoriya predstavleniĭ grupp, Izdat. “Nauka”, Moscow, 1965 (Russian). MR 0209523
G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
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, DOI 10.1017/CBO9780511608759
- 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.
- G. Freud, Orthogonale Polynome, Birkhäuser, Basel, 1969; English transl., Pergamon Press, New York, 1971. MR 0481888
- 4.
- H. Hochstadt, Special functions of mathematical physics, Athena Ser.: Selected Topics in Mathematics, Holt, Rinehart and Winston, New York, 1961. MR 27 #3106. MR 153137
- 5.
- E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Cambridge Univ. Press, Cambridge, 1931; 7th ed., Chelsea, New York, 1955. MR 16, 356. MR 64922
- 6.
- N. N. Lebedev, Special functions and their applications, 2nd rev. ed., Fizmatgiz, Moscow, 1963; English transl., Prentice-Hall, Englewood Cliffs, N.J., 1965. MR 30 #4987; #4988. MR 174795
- 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.
- T. M. MacRobert, Functions of a complex variable, 5th ed., Macmillan, London, 1962. MR 21087
- 9.
- T. M. MacRobert, Spherical harmonics. An elementary treatise on harmonic functions with applications, 3rd rev. ed., prepared with the assistance of I. N. Sneddon, Internat. Ser. of Monographs in Pure and Appl. Math., vol. 98, Pergamon Press, Oxford, 1967. MR 36 #4037. MR 220985
- 10.
- E. B. McBride, Obtaining generating functions, Springer Tracts in Natural Philosophy, vol. 21, Springer-Verlag, New York and Heidelberg, 1971. MR 43 #5077. MR 279355
- 11.
- W. Miller, Jr., Lie theory and special functions, Math. in Sci. and Engineering, vol. 43, Academic Press, New York and London, 1968. MR 41 #8736. MR 264140
- 12.
- F. W. J. Olver, Asymptotics and special functions, Academic Press, New York, 1974. MR 435697
- 13.
- E. D. Rainville, Special functions, Macmillan, New York, 1960. MR 21 #6447. MR 107725
- 14.
- G. Sansone, Orthogonal functions, rev. ed., Pure and Appl. Math., vol. 9, Interscience, New York, 1959. MR 21 #2140. MR 103368
- 15.
- I. N. Sneddon, The special functions of mathematical physics and chemistry, Oliver and Boyd, Edinburgh, 1961. MR 80170
- 16.
- B. Spain and M. G. Smith, Functions of mathematical physics, Van Nostrand Rheinhold, London, 1970.
- 17.
- G. Szegö, Orthogonal polynomials, 3rd ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R.I., 1967. MR 310533
- 18.
- J. D. Talman, Special functions: A group theoretic approach, Benjamin, New York and Amsterdam, 1968. MR 39 #511. MR 239154
- 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 connected with class one representations of groups of motions in spaces of constant curvature, Trudy Moskov. Mat. Obšč. 12 (1963), 185-257 Trans. Moscow Math. Soc. 1963, 209-290. MR 29 #191. MR 162887
- 21.
- N. Ja. Vilenkin, Special functions and the theory of group representations, "Nauka", Moscow, 1965; English transl., Transl. Math. Monographs, vol. 22, Amer. Math. Soc., Providence, R.I., 1968. MR 35 #420; 37 #5429. MR 209523
- 22.
- G. N. Watson, A treatise on the theory of Bessel functions, 2nd ed., Cambridge Univ. Press, Cambridge; Macmillan, New York, 1944. MR 6, 64. MR 10746
- 23.
- E. T. Whittaker and G. N. Watson, A course of modern analysis, 4th ed., Cambridge Univ. Press, London, 1927. MR 1424469
Review Information:
Reviewer:
Ian N. Sneddon
Journal:
Bull. Amer. Math. Soc.
82 (1976), 237-243
DOI:
https://doi.org/10.1090/S0002-9904-1976-14001-3
