In mathematics, Brenke polynomials are special cases of generalized Appell polynomials, and BrenkeâÂÂChihara polynomials are the Brenke polynomials that are also orthogonal polynomials.
introduced sequences of Brenke polynomials P<sub>n</sub>, which are special cases of generalized Appell polynomials with generating function of the form
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. Geronimus (1947) found some further examples of orthogonal Brenke polynomials. completely classified all Brenke polynomials that form orthogonal sequences, which are now called BrenkeâÂÂChihara polynomials, and found their orthogonality relations.