Fa%C3%A0%20di%20Bruno%20formula
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1: 18.42 Software
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►A more complete list of available software for computing these functions, and for generating formulas symbolically, is found in the Software Index.
For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C3).
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2: 20 Theta Functions
Chapter 20 Theta Functions
…3: 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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Un procedimento di calcolo per le funzioni gamma incomplete.
Rend. Sem. Mat. Univ. Politec. Torino 37 (1), pp. 1–9 (Italian).
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WKB and turning point theory for second-order difference equations.
In Spectral Methods for Operators of Mathematical Physics,
Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.
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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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4: 8 Incomplete Gamma and Related
Functions
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5: 28 Mathieu Functions and Hill’s Equation
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6: Gergő Nemes
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►As 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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7: Wolter Groenevelt
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►As 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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8: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
9: 23 Weierstrass Elliptic and Modular
Functions
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10: 36 Integrals with Coalescing Saddles
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