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Thomae transformation


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1: 35.8 Generalized Hypergeometric Functions of Matrix Argument
Thomae Transformation
2: Bibliography G
  • F. Gao and V. J. W. Guo (2013) Contiguous relations and summation and transformation formulae for basic hypergeometric series. J. Difference Equ. Appl. 19 (12), pp. 2029–2042.
  • 3: Bibliography S
  • J. L. Schiff (1999) The Laplace Transform: Theory and Applications. Undergraduate Texts in Mathematics, Springer-Verlag, New York.
  • J. D. Secada (1999) Numerical evaluation of the Hankel transform. Comput. Phys. Comm. 116 (2-3), pp. 278–294.
  • D. Shanks (1955) Non-linear transformations of divergent and slowly convergent sequences. J. Math. Phys. 34, pp. 1–42.
  • O. A. Sharafeddin, H. F. Bowen, D. J. Kouri, and D. K. Hoffman (1992) Numerical evaluation of spherical Bessel transforms via fast Fourier transforms. J. Comput. Phys. 100 (2), pp. 294–296.
  • A. Sidi (2003) Practical Extrapolation Methods: Theory and Applications. Cambridge Monographs on Applied and Computational Mathematics, Vol. 10, Cambridge University Press, Cambridge.
  • 4: Bibliography E
  • U. T. Ehrenmark (1995) The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature. J. Comput. Appl. Math. 61 (1), pp. 43–72.
  • A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1954a) Tables of Integral Transforms. Vol. I. McGraw-Hill Book Company, Inc., New York-Toronto-London.
  • A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1954b) Tables of Integral Transforms. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.
  • Euclid (1908) The Thirteen Books of Euclid’s Elements. Cambridge University Press, Cambridge.
  • W. N. Everitt (1982) On the transformation theory of ordinary second-order linear symmetric differential expressions. Czechoslovak Math. J. 32(107) (2), pp. 275–306.
  • 5: Bibliography B
  • W. N. Bailey (1929) Transformations of generalized hypergeometric series. Proc. London Math. Soc. (2) 29 (2), pp. 495–502.
  • R. Barakat and E. Parshall (1996) Numerical evaluation of the zero-order Hankel transform using Filon quadrature philosophy. Appl. Math. Lett. 9 (5), pp. 21–26.
  • A. P. Bassom, P. A. Clarkson, and A. C. Hicks (1995) Bäcklund transformations and solution hierarchies for the fourth Painlevé equation. Stud. Appl. Math. 95 (1), pp. 1–71.
  • P. Bleher and A. Its (1999) Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. of Math. (2) 150 (1), pp. 185–266.
  • W. G. C. Boyd (1990b) Stieltjes transforms and the Stokes phenomenon. Proc. Roy. Soc. London Ser. A 429, pp. 227–246.