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Book Review
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Book Information
Author(s):
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:
- 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 481888
- 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
Additional Information:
Reviewer(s):
Ian N.
Sneddon
Review Information:
Journal:
Bull. Amer. Math. Soc.
82
(1976),
237-243.
DOI:
10.1090/S0002-9904-1976-14001-3
PII:
S 0002-9904(1976)14001-3
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