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Properties of Partially Degenerate Complex Appell Polynomials

Department of Mathematics, Pusan National University, Busan 46241, Korea
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Symmetry 2019, 11(12), 1508; https://doi.org/10.3390/sym11121508
Received: 29 October 2019 / Revised: 10 December 2019 / Accepted: 10 December 2019 / Published: 11 December 2019
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
Keywords: Appell polynomials; Complex Appell polynomials; degenerate Appell polynomials; degenerate Bernoulli polynomials; degenerate Euler polynomials Appell polynomials; Complex Appell polynomials; degenerate Appell polynomials; degenerate Bernoulli polynomials; degenerate Euler polynomials
MDPI and ACS Style

Kim, D.; Kim, S. Properties of Partially Degenerate Complex Appell Polynomials. Symmetry 2019, 11, 1508.

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