connection%20with%20spheroidal%20wave%0Afunctions
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1: 30.1 Special Notation
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βΊThe main functions treated in this chapter are the eigenvalues and the spheroidal wave functions , , , , and , .
…Meixner and Schäfke (1954) use , , , for , , , , respectively.
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Other Notations
… βΊ2: 30.11 Radial Spheroidal Wave Functions
§30.11 Radial Spheroidal Wave Functions
βΊ§30.11(i) Definitions
… βΊConnection Formulas
… βΊ§30.11(v) Connection with the and Functions
… βΊwhere …3: 30.2 Differential Equations
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§30.2(i) Spheroidal Differential Equation
… βΊIn applications involving prolate spheroidal coordinates is positive, in applications involving oblate spheroidal coordinates is negative; see §§30.13, 30.14. … βΊThe Liouville normal form of equation (30.2.1) is … βΊ§30.2(iii) Special Cases
…4: William P. Reinhardt
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βΊThis is closely connected with his interests in classical dynamical “chaos,” an area where he coauthored a book, Chaos in atomic physics with Reinhold Blümel.
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βΊIn November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
5: 20 Theta Functions
Chapter 20 Theta Functions
…6: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
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7: 25.12 Polylogarithms
8: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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9: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Hill’s Equation.
Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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10: Bibliography L
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The two-point connection problem for differential equations of the Heun class.
Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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The central two-point connection problem for the Heun class of ODEs.
J. Phys. A 31 (18), pp. 4249–4261.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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A partition function connected with the modulus five.
Duke Math. J. 8 (4), pp. 631–655.
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