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1: 20 Theta Functions
Chapter 20 Theta Functions
…2: 8 Incomplete Gamma and Related
Functions
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3: 28 Mathieu Functions and Hill’s Equation
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4: 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.
5: 23 Weierstrass Elliptic and Modular
Functions
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6: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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Bounds for symmetric elliptic integrals.
J. Approx. Theory 122 (2), pp. 249–259.
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Inequalities and bounds for the incomplete gamma function.
Results Math. 63 (3-4), pp. 1209–1214.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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7: 36 Integrals with Coalescing Saddles
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8: 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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9: 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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