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Several addition formulas for a general class of $q$-Appell sequences are proved. The $q$-addition formulas, which are derived, involved not only the generalized $q$-Bernoulli, the generalized $q$-Euler and the generalized $q$-Genocchi polynomials, but also the $q$-Stirling numbers of the second kind and several general families of hypergeometric polynomials. Some $q$-umbral calculus generalizations of the addition formulas are also investigated.
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참고문헌 (21)
참고문헌 신청
W. A. Al-Salam / 1967 / q-Appell polynomials / Ann. Mat. Pura Appl. (4) 77:31~45
I. Area / 2001 / Solving connection and linearization problems within the Askey scheme and its q-analogue via inversion formulas / J. Comput. Appl. Math. 133(1-2):151~162
N. M. Atakishiyev / 1994 / On the Rogers-Szego polynomials / J. Phys. A 27(17):L611~L615
T. Ernst / 2012 / A Comprehensive Treatment of q-Calculus / Birkhauser/Springer Basel AG
J. L. Fields / 1961 / Expansions of hypergeometric functions in hypergeometric functions / Math. Comp. 15:390~395
I. Area / 2001 / Solving connection and linearization problems within the Askey scheme and its q-analogue via inversion formulas / J. Comput. Appl. Math. 133(1-2):151~162
N. M. Atakishiyev / 1994 / On the Rogers-Szego polynomials / J. Phys. A 27(17):L611~L615
T. Ernst / 2012 / A Comprehensive Treatment of q-Calculus / Birkhauser/Springer Basel AG
J. L. Fields / 1961 / Expansions of hypergeometric functions in hypergeometric functions / Math. Comp. 15:390~395
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