Bailey%20pairs
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21—30 of 183 matching pages
21: 18.18 Sums
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►and a similar pair of equations by symmetry; compare the second row in Table 18.6.1.
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►For the Poisson kernel of Jacobi polynomials (the Bailey formula) see Bailey (1938).
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22: 16.12 Products
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23: 17.7 Special Cases of Higher Functions
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-Analog of Bailey’s Sum
… ►First -Analog of Bailey’s Sum
… ►Second -Analog of Bailey’s Sum
… ►Bailey’s Nonterminating Extension of Jackson’s Sum
…24: 8 Incomplete Gamma and Related
Functions
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25: 28 Mathieu Functions and Hill’s Equation
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26: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice.
Phys. A 190 (3-4), pp. 346–362.
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27: 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.
28: 23 Weierstrass Elliptic and Modular
Functions
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29: 24.19 Methods of Computation
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►For number-theoretic applications it is important to compute for ; in particular to find the irregular pairs
for which .
We list here three methods, arranged in increasing order of efficiency.
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30: 16.4 Argument Unity
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►Methods of deriving such identities are given by Bailey (1964), Rainville (1960), Raynal (1979), and Wilson (1978).
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►See Bailey (1964, pp. 19–22).
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►See Raynal (1979), Wilson (1978), and Bailey (1964).
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►See Bailey (1964, §4.4(4)).
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►See Bailey (1964, §§4.3(7) and 7.6(1)) for the transformation formulas and Wilson (1978) for contiguous relations.
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