About the Project
NIST

integral representation

AdvancedHelp

(0.004 seconds)

1—10 of 123 matching pages

1: 10.64 Integral Representations
§10.64 Integral Representations
2: 18.10 Integral Representations
§18.10 Integral Representations
Ultraspherical
Legendre
Jacobi
Ultraspherical
3: 12.18 Methods of Computation
These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions. …
4: 16.25 Methods of Computation
Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations. …
5: 13.12 Products
For integral representations, integrals, and series containing products of M ( a , b , z ) and U ( a , b , z ) see Erdélyi et al. (1953a, §6.15.3).
6: 14.25 Integral Representations
§14.25 Integral Representations
For corresponding contour integrals, with less restrictions on μ and ν , see Olver (1997b, pp. 174–179), and for further integral representations see Magnus et al. (1966, §4.6.1).
7: 25.5 Integral Representations
§25.5 Integral Representations
25.5.5 ζ ( s ) = - s 0 x - x - 1 2 x s + 1 d x , - 1 < s < 0 .
25.5.8 ζ ( s ) = 1 2 ( 1 - 2 - s ) Γ ( s ) 0 x s - 1 sinh x d x , s > 1 .
25.5.19 ζ ( m + s ) = ( - 1 ) m - 1 Γ ( s ) sin ( π s ) π Γ ( m + s ) 0 ψ ( m ) ( 1 + x ) x - s d x , m = 1 , 2 , 3 , .
§25.5(iii) Contour Integrals
8: 24.7 Integral Representations
§24.7 Integral Representations
§24.7(i) Bernoulli and Euler Numbers
24.7.5 B 2 n = ( - 1 ) n 2 n ( 2 n - 1 ) π 0 t 2 n - 2 ln ( 1 - e - 2 π t ) d t .
§24.7(ii) Bernoulli and Euler Polynomials
For further integral representations see Prudnikov et al. (1986a, §§2.3–2.6) and Gradshteyn and Ryzhik (2000, Chapters 3 and 4).
9: 13.25 Products
For integral representations, integrals, and series containing products of M κ , μ ( z ) and W κ , μ ( z ) see Erdélyi et al. (1953a, §6.15.3).
10: 23.11 Integral Representations
§23.11 Integral Representations