# fractional transformations

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## 1—10 of 32 matching pages

##### 2: 19.14 Reduction of General Elliptic Integrals
The last reference gives a clear summary of the various steps involving linear fractional transformations, partial-fraction decomposition, and recurrence relations. …
##### 3: 1.9 Calculus of a Complex Variable
###### Bilinear Transformation
Other names for the bilinear transformation are fractional linear transformation, homographic transformation, and Möbius transformation. …
##### 4: Bibliography H
• P. Henrici (1977) Applied and Computational Complex Analysis. Vol. 2: Special Functions—Integral Transforms—Asymptotics—Continued Fractions. Wiley-Interscience [John Wiley & Sons], New York.
• ##### 5: 15.8 Transformations of Variable
A quadratic transformation relates two hypergeometric functions, with the variable in one a quadratic function of the variable in the other, possibly combined with a fractional linear transformation. …
##### 6: Bibliography K
• T. H. Koornwinder (2015) Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators. SIGMA Symmetry Integrability Geom. Methods Appl. 11, pp. Paper 074, 22.
• ##### 7: Bibliography J
• W. B. Jones and W. Van Assche (1998) Asymptotic behavior of the continued fraction coefficients of a class of Stieltjes transforms including the Binet function. In Orthogonal functions, moment theory, and continued fractions (Campinas, 1996), Lecture Notes in Pure and Appl. Math., Vol. 199, pp. 257–274.
• ##### 8: Bibliography C
• A. D. Chave (1983) Numerical integration of related Hankel transforms by quadrature and continued fraction expansion. Geophysics 48 (12), pp. 1671–1686.
• ##### 9: 15.19 Methods of Computation
For $z\in\mathbb{R}$ it is always possible to apply one of the linear transformations in §15.8(i) in such a way that the hypergeometric function is expressed in terms of hypergeometric functions with an argument in the interval $[0,\frac{1}{2}]$. … When $\Re z>\frac{1}{2}$ it is better to begin with one of the linear transformations (15.8.4), (15.8.7), or (15.8.8). …
###### §15.19(v) Continued Fractions
In Colman et al. (2011) an algorithm is described that uses expansions in continued fractions for high-precision computation of the Gauss hypergeometric function, when the variable and parameters are real and one of the numerator parameters is a positive integer. …
##### 10: 2.6 Distributional Methods
###### §2.6(ii) Stieltjes Transform
The Stieltjes transform of $f(t)$ is defined by … Corresponding results for the generalized Stieltjes transform
###### §2.6(iii) Fractional Integrals
The Riemann–Liouville fractional integral of order $\mu$ is defined by …