Article · Wikipedia archive · Last revised Jul 7, 2026

Denisyuk polynomials

In mathematics, Denisyuk polynomials Den(x) or Mn(x) are generalizations of the Laguerre polynomials introduced by Denisyuk (1954) given by the generating function

Last revised
Jul 7, 2026
Read time
≈ 1 min
Length
138 w
Citations
1
Source

In mathematics, Denisyuk polynomials Den(x) or Mn(x) are generalizations of the Laguerre polynomials introduced by Denisyuk (1954) given by the generating function1

n = 0 t n M n ( x ) = 1 1 + t exp ( x t 1 t ) . {\displaystyle \displaystyle \sum _{n=0}^{\infty }t^{n}M_{n}(x)={\frac {1}{1+t}}\exp \left(-{\frac {xt}{1-t}}\right).}

Notes

Notes

References

References

  • Denisyuk, I. M. (1954), "Some integrals, matrices and approximations connected with polynomials analogous to the Laguerre polynomials", Akademiya Nauk Ukrainskoui SSR. Doklady. Seriya A. Fiziko-Matematicheskie i Tekhnicheskie Nauki (in Ukrainian), 1954: 239–242, ISSN 0201-8446, MR 0067241