homographic transformations
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11: 22.7 Landen Transformations
§22.7 Landen Transformations
►§22.7(i) Descending Landen Transformation
… ►§22.7(ii) Ascending Landen Transformation
… ►§22.7(iii) Generalized Landen Transformations
…12: 16.20 Integrals and Series
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►Extensive lists of Laplace transforms and inverse Laplace transforms of the Meijer -function are given in Prudnikov et al. (1992a, §3.40) and Prudnikov et al. (1992b, §3.38).
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13: 16.6 Transformations of Variable
§16.6 Transformations of Variable
►Quadratic
… ►Cubic
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16.6.2
►For Kummer-type transformations of functions see Miller (2003) and Paris (2005a), and for further transformations see Erdélyi et al. (1953a, §4.5), Miller and Paris (2011), Choi and Rathie (2013) and Wang and Rathie (2013).
14: 17.18 Methods of Computation
§17.18 Methods of Computation
… ►The two main methods for computing basic hypergeometric functions are: (1) numerical summation of the defining series given in §§17.4(i) and 17.4(ii); (2) modular transformations. …15: 27.17 Other Applications
§27.17 Other Applications
►Reed et al. (1990, pp. 458–470) describes a number-theoretic approach to Fourier analysis (called the arithmetic Fourier transform) that uses the Möbius inversion (27.5.7) to increase efficiency in computing coefficients of Fourier series. …16: 19.13 Integrals of Elliptic Integrals
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§19.13(iii) Laplace Transforms
►For direct and inverse Laplace transforms for the complete elliptic integrals , , and see Prudnikov et al. (1992a, §3.31) and Prudnikov et al. (1992b, §§3.29 and 4.3.33), respectively.17: 3.9 Acceleration of Convergence
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§3.9(i) Sequence Transformations
… ►§3.9(ii) Euler’s Transformation of Series
… ►Euler’s transformation is usually applied to alternating series. … ►§3.9(iv) Shanks’ Transformation
… ►§3.9(vi) Applications and Further Transformations
…18: 32.7 Bäcklund Transformations
§32.7 Bäcklund Transformations
… ►Then the transformations … ►The quadratic transformation …The quartic transformation … ►19: 2.6 Distributional Methods
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