Lauricella function

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1: 19.15 Advantages of Symmetry

… ►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

… ►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. …

4: Bibliography C

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Lauricella’s hypergeometric function $F_D$ . J. Math. Anal. Appl. 7 (3), pp. 452–470.

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External Links:

Document, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§19.15, §19.16(iii), §19.18(ii), §19.25(vii), §19.28, §19.28, Profile Bille C. Carlson.

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