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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 , , b n ; z 1 , z 2 , , 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
§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
  • B. C. Carlson (1963) Lauricella’s hypergeometric function F D . J. Math. Anal. Appl. 7 (3), pp. 452–470.