triple%20integrals
(0.001 seconds)
21—30 of 477 matching pages
21: 20.12 Mathematical Applications
…
►For applications of Jacobi’s triple product (20.5.9) to Ramanujan’s function and Euler’s pentagonal numbers see Hardy and Wright (1979, pp. 132–160) and McKean and Moll (1999, pp. 143–145).
…
22: Peter L. Walker
…
►Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004.
…
►
…
23: 7.24 Approximations
…
►
•
►
•
►
•
…
►
•
§7.24(i) Approximations in Terms of Elementary Functions
… ►Cody (1969) provides minimax rational approximations for and . The maximum relative precision is about 20S.
Cody et al. (1970) gives minimax rational approximations to Dawson’s integral (maximum relative precision 20S–22S).
Luke (1969b, vol. 2, pp. 422–435) gives main diagonal Padé approximations for , , , , and ; approximate errors are given for a selection of -values.
24: 20.4 Values at = 0
…
►
Jacobi’s Identity
…25: 25.12 Polylogarithms
…
►The right-hand side is called Clausen’s integral.
…
►
Integral Representation
… ►§25.12(iii) Fermi–Dirac and Bose–Einstein Integrals
►The Fermi–Dirac and Bose–Einstein integrals are defined by … ►In terms of polylogarithms …26: 10.22 Integrals
§10.22 Integrals
►§10.22(i) Indefinite Integrals
… ►§10.22(ii) Integrals over Finite Intervals
… ►Fractional Integral
… ►Triple Products
…27: 22.3 Graphics
28: 34.6 Definition: Symbol
…
►The symbol may also be written as a finite triple sum equivalent to a terminating generalized hypergeometric series of three variables with unit arguments.
…
29: 10.43 Integrals
§10.43 Integrals
►§10.43(i) Indefinite Integrals
… ►§10.43(iii) Fractional Integrals
… ► … ►For infinite integrals of triple products of modified and unmodified Bessel functions, see Gervois and Navelet (1984, 1985a, 1985b, 1986a, 1986b). …30: 10.75 Tables
…
►
•
…
►
•
…
►
•
…
►
•
…
►
•
…
Achenbach (1986) tabulates , , , , , 20D or 18–20S.
Zhang and Jin (1996, p. 270) tabulates , , , , , 8D.
Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
Kerimov and Skorokhodov (1984b) tabulates all zeros of the principal values of and , for , 9S.
Zhang and Jin (1996, p. 271) tabulates , , , , , 8D.