Basic properties are established and generating functions are obtained for the q -Apostol–Euler polynomials. We define q -alternating sums and obtain q -extensions of some formulas from Integral Transform. Spectr. Funct., 20, 377–391 (2009). We also deduce an explicit relationship between the q -Apostol–Euler polynomials and the q -Hurwitz–Lerch zeta-function.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 8, pp. 1104–1117, August, 2013.
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Luo, QM. q-Apostol–Euler Polynomials and q-Alternating Sums. Ukr Math J 65, 1231–1246 (2014). https://doi.org/10.1007/s11253-014-0854-6
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DOI: https://doi.org/10.1007/s11253-014-0854-6