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1: 8.19 Generalized Exponential Integral
§8.19 Generalized Exponential Integral
… ►§8.19(ii) Graphics
… ►§8.19(v) Recurrence Relation and Derivatives
… ►§8.19(ix) Inequalities
… ►§8.19(x) Integrals
…2: 4.2 Definitions
§4.2(iii) The Exponential Function
… ►The function is an entire function of , with no real or complex zeros. … ►3: 6.2 Definitions and Interrelations
§6.2(i) Exponential and Logarithmic Integrals
►The principal value of the exponential integral is defined by … ► is sometimes called the complementary exponential integral. … ► … ►The logarithmic integral is defined by …4: 8.24 Physical Applications
§8.24 Physical Applications
… ►The function appears in: Monte Carlo sampling in statistical mechanics (Kofke (2004)); analysis of packings of soft or granular objects (Prellberg and Owczarek (1995)); growth formulas in cosmology (Hamilton (2001)). ►§8.24(iii) Generalized Exponential Integral
►The function , with , appears in theories of transport and radiative equilibrium (Hopf (1934), Kourganoff (1952), Altaç (1996)). ►With more general values of , supplies fundamental auxiliary functions that are used in the computation of molecular electronic integrals in quantum chemistry (Harris (2002), Shavitt (1963)), and also wave acoustics of overlapping sound beams (Ding (2000)).5: 6.19 Tables
Abramowitz and Stegun (1964, Chapter 5) includes , , , , ; , , , , ; , , , , ; , , , , ; , , . Accuracy varies but is within the range 8S–11S.
Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of , , , 6D; , , , 6D; , , , 6D.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of , , , 8S.
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: Bibliography V
8: 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.
Clenshaw (1962) gives Chebyshev coefficients for for and for (20D).
Luke (1969b, pp. 411–414) gives rational approximations for .