Jump to content

Bender–Dunne polynomials

From Wikipedia, the free encyclopedia

In mathematics, Bender–Dunne polynomials are a two-parameter family of sequences of orthogonal polynomials studied by Carl M. Bender and Gerald V. Dunne.[1][2] They may be defined by the recursion:

,
,

and for :

where and are arbitrary parameters.

References

[edit]
  1. ^ Bender, Carl M.; Dunne, Gerald V. (1988). "Polynomials and operator orderings". Journal of Mathematical Physics. 29 (8): 1727–1731. Bibcode:1988JMP....29.1727B. doi:10.1063/1.527869. ISSN 0022-2488. MR 0955168.
  2. ^ Bender, Carl M.; Dunne, Gerald V. (1996). "Quasi-exactly solvable systems and orthogonal polynomials". Journal of Mathematical Physics. 37 (1): 6–11. arXiv:hep-th/9511138. Bibcode:1996JMP....37....6B. doi:10.1063/1.531373. ISSN 0022-2488. MR 1370155. S2CID 28967621.