hypergeometric%0Afunction
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1: 15.2 Definitions and Analytical Properties
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§15.2(i) Gauss Series
… โบ§15.2(ii) Analytic Properties
… โบThe same properties hold for , except that as a function of , in general has poles at . … โบFor example, when , , and , is a polynomial: …(Both interpretations give solutions of the hypergeometric differential equation (15.10.1), as does , which is analytic at .) …2: 16.2 Definition and Analytic Properties
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§16.2(i) Generalized Hypergeometric Series
… โบ … โบElsewhere the generalized hypergeometric function is a multivalued function that is analytic except for possible branch points at , and . … โบPolynomials
… โบNote also that any partial sum of the generalized hypergeometric series can be represented as a generalized hypergeometric function via …3: 15.10 Hypergeometric Differential Equation
§15.10 Hypergeometric Differential Equation
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15.10.1
โบThis is the hypergeometric differential equation.
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Singularity
… โบ …4: 17.1 Special Notation
§17.1 Special Notation
… โบnonnegative integers. | |
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5: 35.8 Generalized Hypergeometric Functions of Matrix Argument
§35.8 Generalized Hypergeometric Functions of Matrix Argument
โบ§35.8(i) Definition
… โบConvergence Properties
… โบValue at
… โบA similar result for the function of matrix argument is given in Faraut and Korányi (1994, p. 346). …6: 35.7 Gaussian Hypergeometric Function of Matrix Argument
§35.7 Gaussian Hypergeometric Function of Matrix Argument
โบ§35.7(i) Definition
… โบJacobi Form
… โบConfluent Form
… โบSystems of partial differential equations for the (defined in §35.8) and functions of matrix argument can be obtained by applying (35.8.9) and (35.8.10) to (35.7.9). …7: 35.6 Confluent Hypergeometric Functions of Matrix Argument
§35.6 Confluent Hypergeometric Functions of Matrix Argument
โบ§35.6(i) Definitions
… โบLaguerre Form
… โบ§35.6(ii) Properties
… โบ§35.6(iv) Asymptotic Approximations
…8: 19.16 Definitions
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โบwhere () is a real or complex constant, and
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