Lauricella function

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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}\left(b_{1},b_{2},\dots,b_{n};z_{1},z_{2},\dots,z_{n}\right)

(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. …

… ►

… ►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.) …

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. …

… ►See Littler and Fackerell (1975, (2.7)) for an expression of

V_{\boldsymbol{{\nu}}}^{\boldsymbol{{\alpha}}}(\mathbf{x})

in terms of Lauricella’s hypergeometric function

F_{A}

. …

… ►

B. C. Carlson (1963) Lauricella’s hypergeometric function

F_{D}

. J. Math. Anal. Appl. 7 (3), pp. 452–470.

ⓘ

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.
Encodings:: BibTeX

…

… ►See Dunkl and Xu (2014, §5.2.2) for expressions of of these biorthogonal polynomials in terms of Lauricella’s hypergeometric function

F_{B}

. …