# integral representation

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##### 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 $M\left(a,b,z\right)$ and $U\left(a,b,z\right)$ see Erdélyi et al. (1953a, §6.15.3).
##### 6: 14.25 Integral Representations
###### §14.25 IntegralRepresentations
For corresponding contour integrals, with less restrictions on $\mu$ and $\nu$, 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 IntegralRepresentations
25.5.19 $\zeta\left(m+s\right)=(-1)^{m-1}\frac{\Gamma\left(s\right)\sin\left(\pi s% \right)}{\pi\Gamma\left(m+s\right)}\*\int_{0}^{\infty}{\psi}^{(m)}\left(1+x% \right)x^{-s}\mathrm{d}x,$ $m=1,2,3,\dots$.
##### 8: 24.7 Integral Representations
###### §24.7(i) Bernoulli and Euler Numbers
24.7.5 $B_{2n}=(-1)^{n}\frac{2n(2n-1)}{\pi}\*\int_{0}^{\infty}t^{2n-2}\ln\left(1-e^{-2% \pi t}\right)\mathrm{d}t.$
###### §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 $M_{\kappa,\mu}\left(z\right)$ and $W_{\kappa,\mu}\left(z\right)$ see Erdélyi et al. (1953a, §6.15.3).