integral identities
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11—20 of 56 matching pages
11: 35.4 Partitions and Zonal Polynomials
12: 2.6 Distributional Methods
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►On inserting this identity into (2.6.54), we immediately encounter divergent integrals of the form
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13: 15.17 Mathematical Applications
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§15.17(ii) Conformal Mappings
… ►Hypergeometric functions, especially complete elliptic integrals, also play an important role in quasiconformal mapping. … ►§15.17(iv) Combinatorics
►In combinatorics, hypergeometric identities classify single sums of products of binomial coefficients. … ►Quadratic transformations give insight into the relation of elliptic integrals to the arithmetic-geometric mean (§19.22(ii)). …14: 35.6 Confluent Hypergeometric Functions of Matrix Argument
15: 19.7 Connection Formulas
§19.7 Connection Formulas
►§19.7(i) Complete Integrals of the First and Second Kinds
… ►Reciprocal-Modulus Transformation
… ►Provided the functions in these identities are correctly analytically continued in the complex -plane, then the identities will also hold in the complex -plane. ►Imaginary-Modulus Transformation
…16: 22.9 Cyclic Identities
§22.9 Cyclic Identities
… ►§22.9(ii) Typical Identities of Rank 2
… ► ►§22.9(iii) Typical Identities of Rank 3
… ►17: 21.7 Riemann Surfaces
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§21.7(ii) Fay’s Trisecant Identity
… ►where again all integration paths are identical for all components. Generalizations of this identity are given in Fay (1973, Chapter 2). … ►§21.7(iii) Frobenius’ Identity
…18: 6.12 Asymptotic Expansions
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§6.12(i) Exponential and Logarithmic Integrals
… ►For the function see §9.7(i). … ►§6.12(ii) Sine and Cosine Integrals
… ► … ►19: 35.8 Generalized Hypergeometric Functions of Matrix Argument
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35.8.13
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20: 35.7 Gaussian Hypergeometric Function of Matrix Argument
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35.7.5
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