Euler%20integral
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1: Software Index
2: 25.5 Integral Representations
§25.5 Integral Representations
… ►In (25.5.15)–(25.5.19), , is the digamma function, and is Euler’s constant (§5.2). … ►§25.5(iii) Contour Integrals
…3: Bibliography L
4: 20.10 Integrals
§20.10 Integrals
… ►5: 25.20 Approximations
Cody et al. (1971) gives rational approximations for in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are , , , . Precision is varied, with a maximum of 20S.
6: 8.26 Tables
Khamis (1965) tabulates for , to 10D.
§8.26(iv) Generalized Exponential Integral
►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.
7: 25.11 Hurwitz Zeta Function
§25.11(iii) Representations by the Euler–Maclaurin Formula
… ►§25.11(vii) Integral Representations
… ►§25.11(viii) Further Integral Representations
… ►§25.11(ix) Integrals
…8: 25.12 Polylogarithms
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 …9: Bibliography
10: 7.23 Tables
Abramowitz and Stegun (1964, Chapter 7) includes , , , 10D; , , 8S; , , 7D; , , , 6S; , , 10D; , , 9D; , , , 7D; , , , , 15D.
Abramowitz and Stegun (1964, Table 27.6) includes the Goodwin–Staton integral , , 4D; also , , 4D.
Zhang and Jin (1996, pp. 637, 639) includes , , , 8D; , , , 8D.
Zhang and Jin (1996, pp. 638, 640–641) includes the real and imaginary parts of , , , 7D and 8D, respectively; the real and imaginary parts of , , , 8D, together with the corresponding modulus and phase to 8D and 6D (degrees), respectively.
Zhang and Jin (1996, p. 642) includes the first 10 zeros of , 9D; the first 25 distinct zeros of and , 8S.