# triple integrals

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## 7 matching pages

##### 1: 1.5 Calculus of Two or More Variables
###### TripleIntegrals
In case of triple integrals the $(x,y,z)$ sets are of the form …
1.5.43 $\iiint_{D}f(x,y,z)\,\mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z=\iiint_{D^{*}}f(x(u,% v,w),y(u,v,w),z(u,v,w))\*\left|\frac{\partial(x,y,z)}{\partial(u,v,w)}\right|% \,\mathrm{d}u\,\mathrm{d}v\,\mathrm{d}w.$
##### 2: 1.6 Vectors and Vector-Valued Functions
1.6.58 $\iiint_{V}(\nabla\cdot\mathbf{F})\,\mathrm{d}V=\iint_{S}\mathbf{F}\cdot\,% \mathrm{d}\mathbf{S},$
1.6.59 $\iiint_{V}(f\nabla^{2}g+\nabla f\cdot\nabla g)\,\mathrm{d}V=\iint_{S}f\frac{% \partial g}{\partial n}\,\mathrm{d}A,$
1.6.60 $\iiint_{V}(f\nabla^{2}g-g\nabla^{2}f)\,\mathrm{d}V=\iint_{S}\left(f\frac{% \partial g}{\partial n}-g\frac{\partial f}{\partial n}\right)\,\mathrm{d}A,$
##### 3: 22.4 Periods, Poles, and Zeros
This half-period will be plus or minus a member of the triple ${K,iK^{\prime},K+iK^{\prime}}$; the other two members of this triple are quarter periods of $\operatorname{pq}\left(z,k\right)$. …
##### 4: 10.43 Integrals
For infinite integrals of triple products of modified and unmodified Bessel functions, see Gervois and Navelet (1984, 1985a, 1985b, 1986a, 1986b). …
##### 5: 7.13 Zeros
At $z=0$, $C\left(z\right)$ has a simple zero and $S\left(z\right)$ has a triple zero. …
##### 7: Bibliography R
• W. H. Reid (1995) Integral representations for products of Airy functions. Z. Angew. Math. Phys. 46 (2), pp. 159–170.
• W. H. Reid (1997a) Integral representations for products of Airy functions. II. Cubic products. Z. Angew. Math. Phys. 48 (4), pp. 646–655.
• W. H. Reid (1997b) Integral representations for products of Airy functions. III. Quartic products. Z. Angew. Math. Phys. 48 (4), pp. 656–664.
• H. Rosengren (1999) Another proof of the triple sum formula for Wigner $9j$-symbols. J. Math. Phys. 40 (12), pp. 6689–6691.
• G. B. Rybicki (1989) Dawson’s integral and the sampling theorem. Computers in Physics 3 (2), pp. 85–87.