# Lauricella function

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## 4 matching pages

##### 1: 19.15 Advantages of Symmetry

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►Elliptic integrals are special cases of a particular multivariate hypergeometric function called

*Lauricella’s*${F}_{D}$ (Carlson (1961b)). The function ${R}_{-a}({b}_{1},{b}_{2},\mathrm{\dots},{b}_{n};{z}_{1},{z}_{2},\mathrm{\dots},{z}_{n})$ (Carlson (1963)) reveals the full permutation symmetry that is partially hidden in ${F}_{D}$, and leads to symmetric standard integrals that simplify many aspects of theory, applications, and numerical computation. …##### 2: 19.25 Relations to Other Functions

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###### §19.25(vii) Hypergeometric Function

… ►For these results and extensions to the Appell function ${F}_{1}$ (§16.13) and Lauricella’s function ${F}_{D}$ see Carlson (1963). (${F}_{1}$ and ${F}_{D}$ are equivalent to the $R$-function of 3 and $n$ variables, respectively, but lack full symmetry.) …##### 3: Bille C. Carlson

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►In his paper Lauricella’s hypergeometric function
${F}_{D}$
(1963), he defined the $R$-function, a multivariate hypergeometric function that is homogeneous in its variables, each variable being paired with a parameter.
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##### 4: Bibliography C

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Lauricella’s hypergeometric function
${F}_{D}$
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J. Math. Anal. Appl. 7 (3), pp. 452–470.
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