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1: 22.16 Related Functions
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§22.16(i) Jacobi’s Amplitude () Function
►Definition
… ►Quasi-Periodicity
… ►Integral Representation
… ►Special Values
…2: 20 Theta Functions
Chapter 20 Theta Functions
…3: Foreword
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►Much has changed in the years since A&S was published.
…However, we have also seen the birth of a new age of computing technology, which has not only changed how we utilize special functions, but also how we communicate technical information.
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►November 20, 2009
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4: 27.2 Functions
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►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
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27.2.3
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27.2.4
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27.2.14
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5: 19.7 Connection Formulas
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►With ,
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§19.7(ii) Change of Modulus and Amplitude
… ►§19.7(iii) Change of Parameter of
… ►The first of the three relations maps each circular region onto itself and each hyperbolic region onto the other; in particular, it gives the Cauchy principal value of when (see (19.6.5) for the complete case). …6: 8 Incomplete Gamma and Related
Functions
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7: 28 Mathieu Functions and Hill’s Equation
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8: 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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9: 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.
10: 23 Weierstrass Elliptic and Modular
Functions
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