Brenke–Chihara polynomials

Template:Format footnotes In mathematics, Brenke polynomials are special cases of generalized Appell polynomials, and Brenke–Chihara polynomials are the Brenke polynomials that are also orthogonal polynomials.

Template:Harvs introduced sequences of Brenke polynomials P_n, which are special cases of generalized Appell polynomials with generating function of the form

$A(w)B(xw)=\sum _{n=0}^{\mathrm{\infty }}{P}_n(x)w^n.$

Brenke observed that Hermite polynomials and Laguerre polynomials are examples of Brenke polynomials, and asked if there are any other sequences of orthogonal polynomials of this form. Template:Harvtxt found some further examples of orthogonal Brenke polynomials. Template:Harvs completely classified all Brenke polynomials that form orthogonal sequences, which are now called Brenke–Chihara polynomials, and found their orthogonality relations.

References

• Template:Citation
• Template:Citation
• Template:Citation
• Template:Citation

Template:Polynomial-stub