Families of special functions, known from mathematical physics, are defined here by their recursion relations. The operators which raise and lower indices in these functions are considered as generators of a Lie algebra. The general element of the corresponding Lie group thus operates on the function in two ways: on the one hand it shifts the argument of the function; on the other hand it produces an infinite sum of functions (at the unchanged argument) with shifted indices. Equating the two results of the operation gives us ``addition theorems,'' hitherto derived by analytical methods. The present paper restricts itself to the study of 2‐ and 3‐parameter Lie groups.
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Research Article| March 01 1966
Special Functions of Mathematical Physics from the Viewpoint of Lie Algebra
Bruria Kaufman; Special Functions of Mathematical Physics from the Viewpoint of Lie Algebra. J. Math. Phys. 1 March 1966; 7 (3): 447–457. https://doi.org/10.1063/1.1704953
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