About the Project

extensions of Kummer relations


(0.002 seconds)

4 matching pages

1: 16.4 Argument Unity
The other three-term relations are extensions of Kummer’s relations for F 1 2 ’s given in §15.10(ii). … …
2: 13.8 Asymptotic Approximations for Large Parameters
§13.8(ii) Large b and z , Fixed a and b / z
For the parabolic cylinder function U see §12.2, and for an extension to an asymptotic expansion see Temme (1978). …
§13.8(iii) Large a
For an extension to an asymptotic expansion complete with error bounds see Temme (1990b), and for related results see §13.21(i). …
3: Bibliography C
  • B. C. Carlson (2006b) Table of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric R -functions. Math. Comp. 75 (255), pp. 1309–1318.
  • A. D. Chave (1983) Numerical integration of related Hankel transforms by quadrature and continued fraction expansion. Geophysics 48 (12), pp. 1671–1686.
  • C. Chester, B. Friedman, and F. Ursell (1957) An extension of the method of steepest descents. Proc. Cambridge Philos. Soc. 53, pp. 599–611.
  • J. Choi and A. K. Rathie (2013) An extension of a Kummer’s quadratic transformation formula with an application. Proc. Jangjeon Math. Soc. 16 (2), pp. 229–235.
  • W. J. Cody (1991) Performance evaluation of programs related to the real gamma function. ACM Trans. Math. Software 17 (1), pp. 46–54.
  • 4: Bibliography M
  • I. Marquette and C. Quesne (2013) New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems. J. Math. Phys. 54 (10), pp. Paper 102102, 12 pp..
  • I. Marquette and C. Quesne (2016) Connection between quantum systems involving the fourth Painlevé transcendent and k -step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial. J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..
  • M. Micu (1968) Recursion relations for the 3 - j symbols. Nuclear Physics A 113 (1), pp. 215–220.
  • G. J. Miel (1981) Evaluation of complex logarithms and related functions. SIAM J. Numer. Anal. 18 (4), pp. 744–750.
  • E. W. Montroll (1964) Lattice Statistics. In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.), University of California Engineering and Physical Sciences Extension Series, pp. 96–143.