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11: 24.13 Integrals
§24.13(iii) Compendia
For Laplace and inverse Laplace transforms see Prudnikov et al. (1992a, §§3.28.1–3.28.2) and Prudnikov et al. (1992b, §§3.26.1–3.26.2). …
12: 16.5 Integral Representations and Integrals
Laplace transforms and inverse Laplace transforms of generalized hypergeometric functions are given in Prudnikov et al. (1992a, §3.38) and Prudnikov et al. (1992b, §3.36). …
13: 20.10 Integrals
§20.10(ii) Laplace Transforms with respect to the Lattice Parameter
14: 11.7 Integrals and Sums
§11.7(iii) Laplace Transforms
The following Laplace transforms of H ν ( t ) require a > 0 for convergence, while those of L ν ( t ) require a > 1 . …
15: 14.17 Integrals
§14.17(v) Laplace Transforms
For Laplace transforms and inverse Laplace transforms involving associated Legendre functions, see Erdélyi et al. (1954a, pp. 179–181, 270–272), Oberhettinger and Badii (1973, pp. 113–118, 317–324), Prudnikov et al. (1992a, §§3.22, 3.32, and 3.33), and Prudnikov et al. (1992b, §§3.20, 3.30, and 3.31). …
16: 13.10 Integrals
§13.10(ii) Laplace Transforms
For additional Laplace transforms see Erdélyi et al. (1954a, §§4.22, 5.20), Oberhettinger and Badii (1973, §1.17), and Prudnikov et al. (1992a, §§3.34, 3.35). Inverse Laplace transforms are given in Oberhettinger and Badii (1973, §2.16) and Prudnikov et al. (1992b, §§3.33, 3.34). …
17: 2.3 Integrals of a Real Variable
Assume that the Laplace transform
2.3.1 0 e - x t q ( t ) d t
Then
2.3.2 0 e - x t q ( t ) d t s = 0 q ( s ) ( 0 ) x s + 1 , x + .
Then the series obtained by substituting (2.3.7) into (2.3.1) and integrating formally term by term yields an asymptotic expansion: …
18: 16.15 Integral Representations and Integrals
For inverse Laplace transforms of Appell functions see Prudnikov et al. (1992b, §3.40).
19: 10.71 Integrals
For direct and inverse Laplace transforms of Kelvin functions see Prudnikov et al. (1992a, §3.19) and Prudnikov et al. (1992b, §3.19).
20: 9.10 Integrals
§9.10(v) Laplace Transforms
9.10.14 0 e - p t Ai ( t ) d t = e - p 3 / 3 ( 1 3 - p F 1 1 ( 1 3 ; 4 3 ; 1 3 p 3 ) 3 4 / 3 Γ ( 4 3 ) + p 2 F 1 1 ( 2 3 ; 5 3 ; 1 3 p 3 ) 3 5 / 3 Γ ( 5 3 ) ) , p .
9.10.15 0 e - p t Ai ( - t ) d t = 1 3 e p 3 / 3 ( Γ ( 1 3 , 1 3 p 3 ) Γ ( 1 3 ) + Γ ( 2 3 , 1 3 p 3 ) Γ ( 2 3 ) ) , p > 0 ,
9.10.16 0 e - p t Bi ( - t ) d t = 1 3 e p 3 / 3 ( Γ ( 2 3 , 1 3 p 3 ) Γ ( 2 3 ) - Γ ( 1 3 , 1 3 p 3 ) Γ ( 1 3 ) ) , p > 0 .
For Laplace transforms of products of Airy functions see Shawagfeh (1992). …