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1: Bibliography G
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Contiguous relations and summation and transformation formulae for basic hypergeometric series.
J. Difference Equ. Appl. 19 (12), pp. 2029–2042.
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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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Computational aspects of three-term recurrence relations.
SIAM Rev. 9 (1), pp. 24–82.
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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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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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2: 8 Incomplete Gamma and Related
Functions
Chapter 8 Incomplete Gamma and Related Functions
…3: 15.5 Derivatives and Contiguous Functions
§15.5 Derivatives and Contiguous Functions
… βΊ§15.5(ii) Contiguous Functions
βΊThe six functions , , are said to be contiguous to . … βΊAn equivalent equation to the hypergeometric differential equation (15.10.1) is …Further contiguous relations include: …4: 16.3 Derivatives and Contiguous Functions
§16.3 Derivatives and Contiguous Functions
… βΊ§16.3(ii) Contiguous Functions
βΊTwo generalized hypergeometric functions are (generalized) contiguous if they have the same pair of values of and , and corresponding parameters differ by integers. If , then any distinct contiguous functions are linearly related. Examples are provided by the following recurrence relations: …5: 20 Theta Functions
Chapter 20 Theta Functions
…6: 28 Mathieu Functions and Hill’s Equation
Chapter 28 Mathieu Functions and Hill’s Equation
…7: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Interlacing of the zeros of contiguous hypergeometric functions.
Numer. Algorithms 49 (1-4), pp. 387–407.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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8: GergΕ Nemes
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βΊAs of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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9: Wolter Groenevelt
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βΊGroenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems.
βΊAs of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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