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1: William P. Reinhardt
Reinhardt is a theoretical chemist and atomic physicist, who has always been interested in orthogonal polynomials and in the analyticity properties of the functions of mathematical physics. …Older work on the scattering theory of the atomic Coulomb problem led to the discovery of new classes of orthogonal polynomials relating to the spectral theory of Schrödinger operators, and new uses of old ones: this work was strongly motivated by his original ownership of a 1964 hard copy printing of the original AMS 55 NBS Handbook of Mathematical Functions. …
  • In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
    2: Bibliography S
  • A. Sharples (1967) Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
  • I. M. Sheffer (1939) Some properties of polynomial sets of type zero. Duke Math. J. 5, pp. 590–622.
  • I. Sh. Slavutskiĭ (1995) Staudt and arithmetical properties of Bernoulli numbers. Historia Sci. (2) 5 (1), pp. 69–74.
  • R. P. Stanley (1989) Some combinatorial properties of Jack symmetric functions. Adv. Math. 77 (1), pp. 76–115.
  • O. Szász (1951) On the relative extrema of the Hermite orthogonal functions. J. Indian Math. Soc. (N.S.) 15, pp. 129–134.
  • 3: 18.5 Explicit Representations
    §18.5 Explicit Representations
    §18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions
    However, in these circumstances the orthogonality property (18.2.1) disappears. … …
    4: Bibliography R
  • S. Ramanujan (1921) Congruence properties of partitions. Math. Z. 9 (1-2), pp. 147–153.
  • S. Ramanujan (1927) Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.). In Collected Papers,
  • J. Raynal (1979) On the definition and properties of generalized 6 - j  symbols. J. Math. Phys. 20 (12), pp. 2398–2415.
  • W. P. Reinhardt (2018) Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.
  • M. Robnik (1980) An extremum property of the n -dimensional sphere. J. Phys. A 13 (10), pp. L349–L351.
  • 5: Bibliography B
  • G. Backenstoss (1970) Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.
  • P. A. Becker (1997) Normalization integrals of orthogonal Heun functions. J. Math. Phys. 38 (7), pp. 3692–3699.
  • K. L. Bell and N. S. Scott (1980) Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.
  • W. G. Bickley (1935) Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.
  • C. Brezinski (1980) Padé-type Approximation and General Orthogonal Polynomials. International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.
  • 6: Bibliography N
  • W. J. Nellis and B. C. Carlson (1966) Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.
  • G. Nemes (2014b) The resurgence properties of the large order asymptotics of the Anger-Weber function I. J. Class. Anal. 4 (1), pp. 1–39.
  • G. Nemes (2014c) The resurgence properties of the large order asymptotics of the Anger-Weber function II. J. Class. Anal. 4 (2), pp. 121–147.
  • G. Nemes (2015c) The resurgence properties of the incomplete gamma function II. Stud. Appl. Math. 135 (1), pp. 86–116.
  • P. G. Nevai (1979) Orthogonal polynomials. Mem. Amer. Math. Soc. 18 (213), pp. v+185 pp..
  • 7: 14.30 Spherical and Spheroidal Harmonics
    §14.30(ii) Basic Properties
    Most mathematical properties of Y l , m ( θ , ϕ ) can be derived directly from (14.30.1) and the properties of the Ferrers function of the first kind given earlier in this chapter. …
    Orthogonality
    where 𝐚 = ( 1 2 λ λ 2 , i 2 λ i λ 2 , 1 ) and 𝐱 = ( r sin θ cos ϕ , r sin θ sin ϕ , r cos θ ) . …
    8: Bibliography D
  • A. Deaño, J. Segura, and N. M. Temme (2010) Computational properties of three-term recurrence relations for Kummer functions. J. Comput. Appl. Math. 233 (6), pp. 1505–1510.
  • P. A. Deift (1998) Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach. Courant Lecture Notes in Mathematics, Vol. 3, New York University Courant Institute of Mathematical Sciences, New York.
  • B. Döring (1966) Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.
  • K. Driver and K. Jordaan (2013) Inequalities for extreme zeros of some classical orthogonal and q -orthogonal polynomials. Math. Model. Nat. Phenom. 8 (1), pp. 48–59.
  • T. M. Dunster (1989) Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.