Properties of Partially Degenerate Complex Appell Polynomials

Degenerate versions of polynomial sequences have been recently studied to obtain useful properties such as symmetric identities by introducing degenerate exponential-type generating functions. As part of our continued work in degenerate versions of generating functions, we subsequently present our study on degenerate complex Appell polynomials by considering a partially degenerate version of the generating functions of ordinary complex Appell polynomials in this paper. We only consider partially degenerate generating functions to retain the crucial properties of the Appell sequence, and we present useful identities and general properties by splitting complex values into their real and imaginary parts; moreover, we provide several explicit examples. Additionally, the differential equations satisfied by degenerate complex Bernoulli and Euler polynomials are derived by the quasi-monomiality principle using Appell-type polynomials. View Full-Text