TY - JOUR AU - Ghayasuddin, Mohd AU - Sharma, Sunil K. AU - Khan, Waseem A. PY - 2020 TI - A parametric kind of the poly-Bernoulli polynomials JO - Journal of Mathematics and Computer Science SP - 309--321 VL - 21 IS - 4 AB - In this paper, we propose a parametric kind of poly-Bernoulli polynomials by defining the two specific generating functions. We also investigate some analytical properties (for example, summation formulae, differential formulae and relations with other well-known polynomials and numbers) for our introduced polynomials in a systematic way. Furthermore, we derive two interesting connections of our parametric poly-Bernoulli polynomials with the familiar Voigt functions. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.021.04.04 DO - 10.22436/jmcs.021.04.04 ID - Ghayasuddin2020 ER - TY - JOUR TI - On the Lerch zeta function AU - T. M. Apostol JO - Pacific J. Math. PY - 1951 DA - 1951// VL - 1 ID - Apostol1951 ER - TY - JOUR TI - Symmetric identities of Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character $\chi$ AU - S. Araci AU - W. A. Khan AU - K. S. Nisar JO - Symmetry PY - 2018 DA - 2018// VL - 10 ID - Araci2018 ER - TY - JOUR TI - Polylogarithms and poly-Bernoulli polynomials AU - A. Bayad AU - Y. Hamahata JO - Kyushu J. Math. PY - 2011 DA - 2011// VL - 65 ID - Bayad2011 ER - TY - JOUR TI - Truncated Fubini polynomials AU - U. Duran AU - M. Acikgoz JO - Mathematics PY - 2019 DA - 2019// VL - 431 ID - Duran2019 ER - TY - JOUR TI - Hypergeometric Bernoulli polynomials and Appell sequences AU - A. Hassen AU - H. D. Nguyen JO - Int. J. Number Theory PY - 2008 DA - 2008// VL - 4 ID - Hassen2008 ER - TY - JOUR TI - A new class of Laguerre-based Apostol type polynomials AU - W. A. Khan AU - S. Araci AU - M. Acikgoz JO - Cogent Math. PY - 2016 DA - 2016// VL - 3 ID - Khan2016 ER - TY - JOUR TI - Multiple-Poly-Bernoulli polynomials of the second kind associated with Hermite polynomials AU - W. A. Khan AU - M. Ghayasuddin AU - M. Shadab JO - Fasc. Math. PY - 2017 DA - 2017// VL - 58 ID - Khan2017 ER - TY - JOUR TI - A new class of generalized Laguerre-based poly-Bernoulli polynomials AU - W. A. Khan AU - H. Haroon AU - K. S. Nisar AU - T. Kim JO - Global J. Pure Appl. Math. PY - 2017 DA - 2017// VL - 13 ID - Khan2017 ER - TY - JOUR TI - A new class of degenerate Hermite poly-Genocchi polynomials AU - W. A. Khan AU - K. S. Nisar JO - Preprints PY - 2018 DA - 2018// VL - 2018 ID - Khan2018 ER - TY - JOUR TI - Some new classes of generalized Lagrange-Based Apostol type Hermite polynomials AU - W. A. Khan AU - K. S. Nisar JO - J. Ineq. Special Funct. PY - 2019 DA - 2019// VL - 10 ID - Khan2019 ER - TY - JOUR TI - Fully degenerate Hermite poly Bernoulli numbers and polynomials AU - W. A. Khan AU - K. S. Nisar AU - S. Araci AU - M. Acikgoz JO - Adv. Appl. Math. Sci. PY - 2018 DA - 2018// VL - 17 ID - Khan2018 ER - TY - JOUR TI - Multifarious implicit summation formulae of Hermite-Based poly-Daehee polynomials AU - W. A. Khan AU - K. S. Nisar AU - U. Duran AU - M. Acikgoz AU - S. Araci JO - Appl. Math. Inf. Sci. PY - 2018 DA - 2018// VL - 12 ID - Khan2018 ER - TY - JOUR TI - Certain generating function of Hermite-Bernoulli-Laguerre polynomials AU - N. U. Khan AU - T. Usman AU - J. Choi JO - Far East J. Math. Sci. PY - 2017 DA - 2017// VL - 101 ID - Khan2017 ER - TY - JOUR TI - A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials AU - N. U. Khan AU - T. Usman AU - J. Choi JO - Turkish J. Math. PY - 2019 DA - 2019// VL - 43 ID - Khan2019 ER - TY - JOUR TI - A study of generalized Laguerre poly-Genocchi polynomials AU - N. U. Khan AU - T. Usman AU - K. S. Nisar JO - Mathematics PY - 2019 DA - 2019// VL - 7 ID - Khan2019 ER - TY - JOUR TI - A note on degenerate Euler and Bernoulli polynomials of complex variable AU - D. S. Kim AU - T. Kim AU - H. Lee JO - Symmetry PY - 2019 DA - 2019// VL - 11 ID - Kim2019 ER - TY - JOUR TI - Some identities for Euler and Bernoulli polynomials and their zeros AU - T. Kim AU - C. S. Ryoo JO - Axioms PY - 2018 DA - 2018// VL - 7 ID - Kim2018 ER - TY - JOUR TI - Truncated Euler polynomials AU - T. Komatsu AU - C. Pita-Ruiz JO - Math. Slovaca PY - 2018 DA - 2018// VL - 68 ID - Komatsu2018 ER - TY - JOUR TI - A further generalization of the Bernoulli polynomials and on the 2D-Bernoulli polynomials $B_{n}^{2}(x, y)$ AU - B. Kurt JO - Appl. Math. Sci. (Ruse) PY - 2010 DA - 2010// VL - 4 ID - Kurt2010 ER - TY - JOUR TI - Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials AU - Q.-M. Luo AU - H. M. Srivastava JO - J. Math. Anal. Appl. PY - 2005 DA - 2005// VL - 308 ID - Luo2005 ER - TY - JOUR TI - Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials AU - Q.-M. Luo AU - H. M. Srivastava JO - Comput. Math. Appl. PY - 2006 DA - 2006// VL - 51 ID - Luo2006 ER - TY - JOUR TI - $q$-Extensions of some relationships between the Bernoulli and Euler polynomials AU - Q.-M. Luo AU - H. M. Srivastava JO - Taiwanese J. Math. PY - 2011 DA - 2011// VL - 15 ID - Luo2011 ER - TY - JOUR TI - Some implicit summation formulas and symmetric identities for the generalized Hermite-Bernoulli polynomials AU - M. A. Pathan AU - W. A. Khan JO - Mediterr. J. Math. PY - 2015 DA - 2015// VL - 12 ID - Pathan2015 ER - TY - BOOK TI - Special functions AU - E. D. Rainville PB - Macmillan Co. PY - 1971 DA - 1971// CY - New York ID - Rainville1971 ER - TY - JOUR TI - Uber die emission, absorption and intensitats vertcitung von spektrallicien AU - F. Reiche JO - Ber. Deutsch. Phys. Ges. PY - 1913 DA - 1913// VL - 15 ID - Reiche1913 ER - TY - JOUR TI - Some formulas for the Bernoulli and Euler polynomials at rational arguments AU - H. M. Srivastava JO - Math. Proc. Cambridge Philos. Soc. PY - 2000 DA - 2000// VL - 129 ID - Srivastava2000 ER - TY - JOUR TI - A parametric kind of the Fubini-type polynomials AU - H. M. Srivastava AU - C. Kizilates JO - Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM PY - 2019 DA - 2019// VL - 113 ID - Srivastava2019 ER - TY - BOOK TI - A treatise on generating functions AU - H. M. Srivastava AU - H. L. Manocha PB - John Wiley & Sons PY - 1984 DA - 1984// CY - New York ID - Srivastava1984 ER - TY - JOUR TI - A parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi AU - H. M. Srivastava AU - M. Masjed-Jamei AU - M. R. Beyki JO - Appl. Math. Inform. Sci. PY - 2018 DA - 2018// VL - 12 ID - Srivastava2018 ER -