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1: 20 Theta Functions
Chapter 20 Theta Functions
…2: 3.8 Nonlinear Equations
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►(More precisely, is the largest of the possible set of indices for (3.8.3).)
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►This is an iterative method for real twice-continuously differentiable, or complex analytic, functions:
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►From this graph we estimate an initial value .
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►Consider and .
We have and .
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3: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Pagurova (1963) tabulates and (with different notation) for , to 7D.
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.
4: 32.1 Special Notation
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►Unless otherwise noted, primes indicate derivatives with respect to the argument.
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integers. | |
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5: 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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6: 6.16 Mathematical Applications
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6.16.2
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6.16.3
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6.16.4
,
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►This nonuniformity of convergence is an illustration of the Gibbs
phenomenon.
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7: 11.14 Tables
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►Tables listed in these Indices are omitted from the subsections that follow.
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Zhang and Jin (1996) tabulates and for and to 8D or 7S.
Agrest and Maksimov (1971, Chapter 11) defines incomplete Struve, Anger, and Weber functions and includes tables of an incomplete Struve function for , , and , together with surface plots.
8: 28.1 Special Notation
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integers. | |
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order of the Mathieu function or modified Mathieu function. (When is an integer it is often replaced by .) | |
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primes | unless indicated otherwise, derivatives with respect to the argument |
Abramowitz and Stegun (1964, Chapter 20)
…9: 36 Integrals with Coalescing Saddles
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10: Wolter Groenevelt
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► 1976 in Leidschendam, the Netherlands) is an Associate Professor at the Delft University of Technology in Delft, The Netherlands.
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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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