# The q-Heun operator of big q-Jacobi type and the q-Heun algebra

* Corresponding author
Abstract : The q-Heun operator of the big q-Jacobi type on the exponential grid is defined. This operator is the most general second order q-difference operator that maps polynomials of degree $n$ to polynomials of degree $n+1$. It is tridiagonal in bases made out of either q-Pochhammer or big q-Jacobi polynomials and is bilinear in the operators of the q-Hahn algebra. The extension of this algebra that includes the q-Heun operator as generator is described. Biorthogonal Pastro polynomials are shown to satisfy a generalized eigenvalue problem or equivalently to be in the kernel of a special linear pencil made out of two q-Heun operators. The special case of the q-Heun operator associated to the little q-Jacobi polynomials is also treated.
Keywords :
Document type :
Journal articles
Domain :

Cited literature [21 references]

https://hal.archives-ouvertes.fr/hal-02143736
Contributor : Sandrine Renard-Riccetti <>
Submitted on : Wednesday, May 29, 2019 - 3:27:43 PM
Last modification on : Wednesday, October 14, 2020 - 4:18:23 AM

### File

1808.06695.pdf
Files produced by the author(s)

### Citation

Pascal Baseilhac, Luc Vinet, Alexei Zhedanov. The q-Heun operator of big q-Jacobi type and the q-Heun algebra. Ramanujan Journal, Springer Verlag, 2019, ⟨10.1007/s11139-018-0106-8⟩. ⟨hal-02143736⟩

Record views