About the Project

Laplace integral

AdvancedHelp

(0.002 seconds)

1—10 of 53 matching pages

1: 6.14 Integrals
§6.14(i) Laplace Transforms
2: 19.13 Integrals of Elliptic Integrals
§19.13(iii) Laplace Transforms
For direct and inverse Laplace transforms for the complete elliptic integrals K ( k ) , E ( k ) , and D ( k ) see Prudnikov et al. (1992a, §3.31) and Prudnikov et al. (1992b, §§3.29 and 4.3.33), respectively.
3: 7.14 Integrals
Laplace Transforms
Laplace Transforms
7.14.5 0 e a t C ( t ) d t = 1 a f ( a π ) , a > 0 ,
7.14.7 0 e a t C ( 2 t π ) d t = ( a 2 + 1 + a ) 1 2 2 a a 2 + 1 , a > 0 ,
7.14.8 0 e a t S ( 2 t π ) d t = ( a 2 + 1 a ) 1 2 2 a a 2 + 1 , a > 0 .
4: 10.71 Integrals
5: 2.3 Integrals of a Real Variable
Assume that the Laplace transform
2.3.1 0 e x t q ( t ) d t
2.3.2 0 e x t q ( t ) d t s = 0 q ( s ) ( 0 ) x s + 1 , x + .
§2.3(iii) Laplace’s Method
These references and Wong (1989, Chapter 2) also contain examples. …
6: 16.5 Integral Representations and Integrals
7: 2.4 Contour Integrals
For examples and extensions (including uniformity and loop integrals) see Olver (1997b, Chapter 4), Wong (1989, Chapter 1), and Temme (1985). …
2.4.2 Q ( z ) = 0 e z t q ( t ) d t
2.4.5 q ( t ) = 1 2 π i σ i σ + i e t z Q ( z ) d z , 0 < t < ,
For examples see Olver (1997b, pp. 315–320).
§2.4(iii) Laplace’s Method
8: 35.4 Partitions and Zonal Polynomials
Laplace and Beta Integrals
9: 14.17 Integrals
§14.17(v) Laplace Transforms
10: 19.18 Derivatives and Differential Equations
The next four differential equations apply to the complete case of R F and R G in the form R a ( 1 2 , 1 2 ; z 1 , z 2 ) (see (19.16.20) and (19.16.23)). … and U = R a ( 1 2 , 1 2 ; z + i ρ , z i ρ ) , with ρ = x 2 + y 2 , satisfies Laplace’s equation: …