Lie Theory and Generalizations of the Hypergeometric Functions

DOI10.1137/0125026zbMath0269.33007OpenAlexW2014352967MaRDI QIDQ5686296

Willard jun. Miller

Publication date: 1973

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0125026

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (18)

Associated Legendre functions and spherical harmonics of fractional degree and order ⋮ On contiguity relations of the confluent hypergeometric systems ⋮ The Lauricella functions and exact string scattering amplitudes ⋮ Models of Lie algebra \(sl(2, \mathbb{C})\) and special matrix functions by means of a matrix integral transformation ⋮ The string BCJ relations revisited and extended recurrence relations of nonrelativistic string scattering amplitudes ⋮ Contiguous relations and their computations for \(_2F_1\) hypergeometric series ⋮ The $\operatorname{SL}(K + 3, \mathbb{C})$ symmetry of the bosonic string scattering amplitudes ⋮ Contiguous relations for \(_{2}F_{1}\) hypergeometric series ⋮ Solving Lauricella string scattering amplitudes through recurrence relations ⋮ Lie symmetries of finite-difference equations ⋮ The Lie theory of hypergeometric functions arising from \((1-\sum^ k_{i=1}z_ i)^ \lambda(1-\sum^ r_{j=k+1}z_ j)^ -\lambda\) ⋮ Gröbner basis and the problem of contiguous relations ⋮ On some new contiguous relations for the Gauss hypergeometric function with applications ⋮ On the contiguous relations of hypergeometric series ⋮ A generalization of the Gauß hypergeometric series ⋮ Characteristic functionals of Dirichlet measures ⋮ From conformal group to symmetries of hypergeometric type equations ⋮ Contiguity relations for \(q\)-hypergeometric function and related quantum group

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