multidimensional integrals

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1: 5.14 Multidimensional Integrals
§5.14 MultidimensionalIntegrals
5.14.7 $\frac{1}{(2\pi)^{n}}\int_{[-\pi,\pi]^{n}}\prod_{1\leq j $\Re b>-1/n$.
2: 2.5 Mellin Transform Methods
The first reference also contains explicit expressions for the error terms, as do Soni (1980) and Carlson and Gustafson (1985). The Mellin transform method can also be extended to derive asymptotic expansions of multidimensional integrals having algebraic or logarithmic singularities, or both; see Wong (1989, Chapter 3), Paris and Kaminski (2001, Chapter 7), and McClure and Wong (1987). …
3: 35.8 Generalized Hypergeometric Functions of Matrix Argument
Multidimensional Mellin–Barnes integrals are established in Ding et al. (1996) for the functions ${{}_{p}F_{q}}$ and ${{}_{p+1}F_{p}}$ of matrix argument. …These multidimensional integrals reduce to the classical Mellin–Barnes integrals5.19(ii)) in the special case $m=1$. …
 $g,h$ positive integers. … line integral of the differential $\omega$ over the cycle $a$.
The function $\Theta(\boldsymbol{{\phi}}|\mathbf{B})=\theta\left(\boldsymbol{{\phi}}/(2\pi i% )\middle|\mathbf{B}/(2\pi i)\right)$ is also commonly used; see, for example, Belokolos et al. (1994, §2.5), Dubrovin (1981), and Fay (1973, Chapter 1).
As in §20.11(ii), the modulus $k$ of elliptic integrals19.2(ii)), Jacobian elliptic functions (§22.2), and Weierstrass elliptic functions (§23.6(ii)) can be expanded in $q$-series via (20.9.1). … Multidimensional theta functions with characteristics are defined in §21.2(ii) and their properties are described in §§21.3(ii), 21.5(ii), and 21.6. …