@Article{Araci2014, author="S. Araci", title="Novel identities involving Genocchi numbers and polynomials arising from applications of umbral calculus", journal="Appl. Math. Comput.", year="2014", pages=" 599–607. ", volume="233" } @Article{Araci2013 , author="S. Araci, M. Acikgoz, A. Kilicman", title="Extended p-adic q-invariant integrals on \(\mathbb{Z}_p\) associated with applications of umbral calculus", journal="Adv. Difference Equ.", year="2013 ", pages="14 pages. ", volume="2013 " } @Article{Araci2013, author="S. Araci, M. Acikgoz, E. Sen", title="On the extended Kim’s p-adic q-deformed fermionic integrals in the p-adic integer ring", journal="J. Number Theory", year="2013", pages="3348–3361. ", volume="133" } @Article{Araci2014, author=" S. Araci, M. Acikgoz, J. J. Seo", title="A new family of q-analogue of Genocchi numbers and polynomials of higher order", journal="Kyungpook Math. J.", year="2014", pages="131–141. ", volume="54" } @Article{Bagdasaryan2010, author="A. G. Bagdasaryan", title="An elementary and real approach to values of the Riemann zeta function", journal="Phys. Atom. Nucl.", year="2010", pages=" 251–254.", volume="73" } @Article{Choi2008, author="J.-S. Choi, P. J. Anderson, H. M. Srivastava", title="Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta function", journal="Appl. Math. Comput.", year="2008", pages="723–737. ", volume="199" } @Article{Choi2009, author="J.-S. Choi, P. J. Anderson, H. M. Srivastava", title="Carlitz’s q-Bernoulli and q-Euler numbers and polynomials and a class of generalized q-Hurwitz zeta functions", journal="Appl. Math. Comput.", year="2009", pages="1185–1208. ", volume="215" } @Article{Dere2013, author=" R. Dere, Y. Simsek, H. M. Srivastava", title="A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra", journal="J. Number Theory", year="2013", pages=" 3245–3263. ", volume="133" } @Article{Ihrig1981, author=" E. C. Ihrig, M. E. H. Ismail", title="A q-umbral calculus", journal=" J. Math. Anal. Appl.", year="1981", pages="178–207. ", volume="84" } @Article{Ismail2002, author="M. E. H. Ismail, M. Rahman", title=" Inverse operators, q-fractional integrals, and q-Bernoulli polynomials", journal="J. Approx. Theory", year="2002", pages="269–307.", volume="114" } @Article{Kim2006, author="T. Kim", title="q-generalized Euler numbers and polynomials", journal="Russ. J. Math. Phys.", year="2006", pages="293–298. ", volume="13" } @Article{Kim2014, author="D. S. Kim, T. Kim", title="q-Bernoulli polynomials and q-umbral calculus", journal="Sci. China Math.", year="2014", pages="1867–1874. ", volume="57" } @Article{Kim2014 , author=" D. S. Kim, T. Kim", title="Some identities of q-Euler polynomials arising from q-umbral calculus", journal="J. Inequal. Appl.", year="2014 ", pages="12 pages. ", volume="2014 " } @Article{Kim2015, author="D. S. Kim, T. Kim", title="Umbral calculus associated with Bernoulli polynomials", journal="J. Number Theory", year="2015", pages="871–882. ", volume="147" } @Article{Kim2013, author="D. S. Kim, T. Kim, S.-H. Lee, J.-J. Seo", title="A note on q-Frobenius-Euler numbers and polynomials", journal=" Adv. Studies Theor. Phys.", year="2013", pages="881–889. ", volume="7" } @Article{Kim2013 , author="T. Kim, T. Mansour, S.-H. Rim, S.-H. Lee", title="Apostol-Euler polynomials arising from umbral calculus", journal=" Adv. Difference Equ.", year="2013 ", pages=" 7 pages. ", volume="2013 " } @Article{Kupershmidt2005, author="B. A. Kupershmidt", title="Reflection symmetries of q-Bernoulli polynomials", journal="J. Nonlinear Math. Phys.", year="2005", pages="412–422. ", volume="12" } @Article{Luo2008, author="Q.-M. Luo", title="The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order", journal=" Integral Transforms Spec. Funct.", year="2008", pages="377–391. ", volume="20" } @Article{Mahmudov2013, author=" N. I. Mahmudov", title=" On a class of q-Bernoulli and q-Euler polynomials", journal=" Adv. Difference Equ.", year="2013", pages="11 pages. ", volume="2013" } @Article{Mahmudov2013 , author=" N. I. Mahmudov, M. E. Keleshteri", title="On a class of generalized q-Bernoulli and q-Euler polynomials", journal="Adv. Difference Equ.", year="2013 ", pages="10 pages.", volume="2013 " } @Article{Pintér2013, author=" Á . Pintér, H. M. Srivastava", title="Addition theorems for the Appell polynomials and the associated classes of polynomial expansions", journal="Aequationes Math.", year="2013", pages="483–495. ", volume="85" } @Article{Rim2012, author="S.-H. Rim, J.-H. Jeong", title="On the modified q-Euler numbers of higher order with weight", journal="Adv. Stud. Contemp. Math. (Kyungshang)", year="2012", pages=" 93–98. ", volume="22" } @Article{Roman1982, author="S. Roman", title="The theory of the umbral calculus, I", journal="J. Math. Anal. Appl.", year="1982", pages="58–115. ", volume="87" } @Article{Roman1983, author="S. Roman", title="The theory of the umbral calculus, III", journal="J. Math. Anal. Appl.", year="1983", pages="528–563. ", volume="95" } @Book{Roman1984, author=" S. Roman", title="The umbral calculus", year="1984", publisher=" Pure and Applied Mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers]", address=" New York" } @Article{Roman1985, author=" S. Roman", title=" More on the umbral calculus, with emphasis on the q-umbral calculus", journal=" J. Math. Anal. Appl.", year="1985", pages="222–254. ", volume="107" } @Article{Sen2013, author=" E. Sen", title="Theorems on Apostol-Euler polynomials of higher order arising from Euler basis", journal="Adv. Stud. Contemp. Math. (Kyungshang)", year="2013", pages=" 337–345. ", volume="23" } @Article{Srivastava2011, author=" H. M. Srivastava,/ ", title="Some generalizations and basic (or q-) extensions of the Bernoulli", journal=" Euler and Genocchi polynomials, Appl. Math. Inf. Sci.", year="2011", pages="390–444. ", volume="5" } @Book{Srivastava2012, author="H. M. Srivastava, J.-S. Choi", title=" Zeta and q-Zeta functions and associated series and integrals", year="2012", publisher="Elsevier, Inc.", address="Amsterdam" }