About the Project

degenerate

AdvancedHelp

(0.001 seconds)

1—10 of 16 matching pages

1: Bille C. Carlson
►Symmetric integrals and their degenerate cases allow greatly shortened integral tables and improved algorithms for numerical computation. …
2: 34.4 Definition: 6 ⁢ j Symbol
►Except in degenerate cases the combination of the triangle inequalities for the four 3 ⁢ j symbols in (34.4.1) is equivalent to the existence of a tetrahedron (possibly degenerate) with edges of lengths j 1 , j 2 , j 3 , l 1 , l 2 , l 3 ; see Figure 34.4.1. …
3: 24.16 Generalizations
►
Degenerate Bernoulli Numbers
4: Bibliography H
►
  • P. I. Hadži (1969) Certain integrals that contain a probability function and degenerate hypergeometric functions. Bul. Akad. S̆tiince RSS Moldoven 1969 (2), pp. 40–47 (Russian).
  • ►
  • F. T. Howard (1996a) Explicit formulas for degenerate Bernoulli numbers. Discrete Math. 162 (1-3), pp. 175–185.
  • 5: 19.16 Definitions
    ►Just as the elementary function R C ⁡ ( x , y ) 19.2(iv)) is the degenerate case …and R D is a degenerate case of R J , so is R J a degenerate case of the hyperelliptic integral, …
    6: 34.2 Definition: 3 ⁢ j Symbol
    ►They must form the sides of a triangle (possibly degenerate). …
    7: Bibliography
    ►
  • V. I. Arnol’d (1972) Normal forms of functions near degenerate critical points, the Weyl groups A k , D k , E k and Lagrangian singularities. Funkcional. Anal. i Priložen. 6 (4), pp. 3–25 (Russian).
  • ►
  • V. I. Arnol’d (1974) Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).
  • 8: Bibliography K
    ►
  • A. V. Kitaev and A. H. Vartanian (2004) Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.
  • ►
  • T. H. Koornwinder and M. Mazzocco (2018) Dualities in the q -Askey scheme and degenerate DAHA. Stud. Appl. Math. 141 (4), pp. 424–473.
  • 9: 19.24 Inequalities
    ►The same reference also gives upper and lower bounds for symmetric integrals in terms of their elementary degenerate cases. …
    10: 22.5 Special Values
    ►In these cases the elliptic functions degenerate into elementary trigonometric and hyperbolic functions, respectively. …