generating%20functions
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1: 26.14 Permutations: Order Notation
2: 26.5 Lattice Paths: Catalan Numbers
3: 26.10 Integer Partitions: Other Restrictions
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§26.10(ii) Generating Functions
… ►where the last right-hand side is the sum over of the generating functions for partitions into distinct parts with largest part equal to . … ►§26.10(vi) Bessel-Function Expansion
… ►where is the modified Bessel function (§10.25(ii)), and … ►
26.10.19
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4: 14.30 Spherical and Spheroidal Harmonics
§14.30 Spherical and Spheroidal Harmonics
… ►Most mathematical properties of can be derived directly from (14.30.1) and the properties of the Ferrers function of the first kind given earlier in this chapter. … ►Herglotz generating function
►The following is the Herglotz generating function … ►5: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
6: 26.3 Lattice Paths: Binomial Coefficients
7: Bibliography G
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Orthogonal Polynomials: Computation and Approximation.
Numerical Mathematics and Scientific Computation, Oxford University Press, New York.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mathieu functions.
Trans. Camb. Philos. Soc. 23, pp. 303–336.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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8: Bibliography B
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The generating function of Jacobi polynomials.
J. London Math. Soc. 13, pp. 8–12.
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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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A short table of the functions
, from to
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Phil. Mag. Series 7 20, pp. 343–347.
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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 C
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The hypergeometric function and the -function near their branch points.
Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 63–89.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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On a generalization of the generating function for Gegenbauer polynomials.
Integral Transforms Spec. Funct. 24 (10), pp. 807–816.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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