integrals of
(0.007 seconds)
11—20 of 421 matching pages
11: 19.35 Other Applications
…
►
§19.35(i) Mathematical
►Generalizations of elliptic integrals appear in analysis of modular theorems of Ramanujan (Anderson et al. (2000)); analysis of Selberg integrals (Van Diejen and Spiridonov (2001)); use of Legendre’s relation (19.7.1) to compute to high precision (Borwein and Borwein (1987, p. 26)). ►§19.35(ii) Physical
… ►12: 6.1 Special Notation
…
►Unless otherwise noted, primes indicate derivatives with respect to the argument.
►The main functions treated in this chapter are the exponential integrals
, , and ; the logarithmic integral
; the sine integrals
and ; the cosine integrals
and .
13: 25.7 Integrals
§25.7 Integrals
►For definite integrals of the Riemann zeta function see Prudnikov et al. (1986b, §2.4), Prudnikov et al. (1992a, §3.2), and Prudnikov et al. (1992b, §3.2).14: 36.3 Visualizations of Canonical Integrals
§36.3 Visualizations of Canonical Integrals
►§36.3(i) Canonical Integrals: Modulus
► … ► ►§36.3(ii) Canonical Integrals: Phase
…15: 6.14 Integrals
§6.14 Integrals
►§6.14(i) Laplace Transforms
… ►§6.14(ii) Other Integrals
… ►
6.14.6
…
►For collections of integrals, see Apelblat (1983, pp. 110–123), Bierens de Haan (1939, pp. 373–374, 409, 479, 571–572, 637, 664–673, 680–682, 685–697), Erdélyi et al. (1954a, vol. 1, pp. 40–42, 96–98, 177–178, 325), Geller and Ng (1969), Gradshteyn and Ryzhik (2000, §§5.2–5.3 and 6.2–6.27), Marichev (1983, pp. 182–184), Nielsen (1906b), Oberhettinger (1974, pp. 139–141), Oberhettinger (1990, pp. 53–55 and 158–160), Oberhettinger and Badii (1973, pp. 172–179), Prudnikov et al. (1986b, vol. 2, pp. 24–29 and 64–92), Prudnikov et al. (1992a, §§3.4–3.6), Prudnikov et al. (1992b, §§3.4–3.6), and Watrasiewicz (1967).
16: 6.17 Physical Applications
§6.17 Physical Applications
►Geller and Ng (1969) cites work with applications from diffusion theory, transport problems, the study of the radiative equilibrium of stellar atmospheres, and the evaluation of exchange integrals occurring in quantum mechanics. …Lebedev (1965) gives an application to electromagnetic theory (radiation of a linear half-wave oscillator), in which sine and cosine integrals are used.17: 6.5 Further Interrelations
18: 6.3 Graphics
19: 19.13 Integrals of Elliptic Integrals
§19.13 Integrals of Elliptic Integrals
… ►For definite and indefinite integrals of complete elliptic integrals see Byrd and Friedman (1971, pp. 610–612, 615), Prudnikov et al. (1990, §§1.11, 2.16), Glasser (1976), Bushell (1987), and Cvijović and Klinowski (1999). ►For definite and indefinite integrals of incomplete elliptic integrals see Byrd and Friedman (1971, pp. 613, 616), Prudnikov et al. (1990, §§1.10.2, 2.15.2), and Cvijović and Klinowski (1994). … ►§19.13(iii) Laplace Transforms
►For direct and inverse Laplace transforms for the complete elliptic integrals , , and see Prudnikov et al. (1992a, §3.31) and Prudnikov et al. (1992b, §§3.29 and 4.3.33), respectively.20: 6.20 Approximations
…
►
•
►
•
►
•
►
•
…
►
•
…
Cody and Thacher (1968) provides minimax rational approximations for , with accuracies up to 20S.
Cody and Thacher (1969) provides minimax rational approximations for , with accuracies up to 20S.
MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions and , with accuracies up to 20S.
Luke and Wimp (1963) covers for (20D), and and for (20D).