# integral representation

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## 21—30 of 124 matching pages

##### 25: 14.12 Integral Representations
###### §14.12(i) $-1
14.12.3 $\mathsf{Q}^{\mu}_{\nu}\left(\cos\theta\right)=\frac{\pi^{1/2}\Gamma\left(\nu+% \mu+1\right)(\sin\theta)^{\mu}}{2^{\mu+1}\Gamma\left(\mu+\frac{1}{2}\right)% \Gamma\left(\nu-\mu+1\right)}\*\left(\int_{0}^{\infty}\frac{(\sinh t)^{2\mu}}{% (\cos\theta+i\sin\theta\cosh t)^{\nu+\mu+1}}\mathrm{d}t+\int_{0}^{\infty}\frac% {(\sinh t)^{2\mu}}{(\cos\theta-i\sin\theta\cosh t)^{\nu+\mu+1}}\mathrm{d}t% \right),$ $0<\theta<\pi$, $\Re\mu>-\tfrac{1}{2}$, $\Re\nu\pm\mu>-1$.
###### §14.12(ii) $1
For further integral representations see Erdélyi et al. (1953a, pp. 158–159) and Magnus et al. (1966, pp. 184–190), and for contour integrals and other representations see §14.25.
##### 26: 1.17 Integral and Series Representations of the Dirac Delta
###### §1.17(ii) IntegralRepresentations
Then comparison of (1.17.2) and (1.17.9) yields the formal integral representation
##### 27: 15.6 Integral Representations
###### §15.6 IntegralRepresentations
The function $\mathbf{F}\left(a,b;c;z\right)$ (not $F\left(a,b;c;z\right)$) has the following integral representations: …
##### 29: 35.9 Applications
For applications of the integral representation (35.5.3) see McFarland and Richards (2001, 2002) (statistical estimation of misclassification probabilities for discriminating between multivariate normal populations). …
##### 30: 9.11 Products
###### §9.11(iii) IntegralRepresentations
For an integral representation of the Dirac delta involving a product of two $\mathrm{Ai}$ functions see §1.17(ii). For further integral representations see Reid (1995, 1997a, 1997b). …