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More on the umbral calculus, with emphasis on the \(q\)-umbral calculus. (English) Zbl 0654.05004

Summary: The interrelationship between distinct umbral calculi is studied. These ideas are applied in particular to \(q\)-umbral calculus, which shows how Andrews’ \(q\)-theory relates to the \(q\)-theory discussed in the previous paper by the author. The \(q\)-Hermite polynomials and basic hypergeometric series are briefly discussed.

MSC:

05A40 Umbral calculus
05A30 \(q\)-calculus and related topics
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
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References:

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