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Calculating zeros of the twisted q-Genocchi polynomials
유천성,김태균 장전수학회 2009 Proceedings of the Jangjeon mathematical society Vol.12 No.3
In this paper we construct the twisted q-Genocchi numbers Gn,q,w and polynomials Gn,q,w(x). We also observe the behavior of complex roots of the the twisted q-Genocchi polynomials Gn,q,w(x), using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the twisted q-Genocchi polynomials Gn,q,w(x). Finally, we give a table for the solutions of the twisted q-Genocchi polynomials..
Sadjang, Patrick Njionou Korean Mathematical Society 2018 대한수학회지 Vol.55 No.5
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.
Patrick Njionou Sadjang 대한수학회 2018 대한수학회지 Vol.55 No.5
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.
CERTAIN RESULTS ON THE q-GENOCCHI NUMBERS AND POLYNOMIALS
서종진 충청수학회 2013 충청수학회지 Vol.26 No.1
In this work, we deal with q-Genocchi numbers and polynomials. We derive not only new but also interesting properties of the q-Genocchi numbers and polynomials. Also, we give Cauchy-type integral formula of the q-Genocchi polynomials and derive distribution formula for the q-Genocchi polynomials. In the ¯nal part, we introduce a de¯nition of q-Zeta-type function which is interpolation function of the q-Genocchi polynomials at negative integers which we express in the present paper.
A NEW CLASS OF q-HERMITE-BASED APOSTOL TYPE FROBENIUS GENOCCHI POLYNOMIALS
Kang, Jung Yoog,Khan, Waseem A. Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.3
In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Genocchi polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Furthermore, we consider some relationships for q-Hermite based Apostol type Frobenius-Genocchi polynomials of order α associated with q-Apostol Bernoulli polynomials, q-Apostol Euler polynomials and q-Apostol Genocchi polynomials.
CERTAIN RESULTS ON THE q-GENOCCHI NUMBERS AND POLYNOMIALS
Seo, Jong Jin Chungcheong Mathematical Society 2013 충청수학회지 Vol.26 No.1
In this work, we deal with $q$-Genocchi numbers and polynomials. We derive not only new but also interesting properties of the $q$-Genocchi numbers and polynomials. Also, we give Cauchy-type integral formula of the $q$-Genocchi polynomials and derive distribution formula for the $q$-Genocchi polynomials. In the final part, we introduce a definition of $q$-Zeta-type function which is interpolation function of the $q$-Genocchi polynomials at negative integers which we express in the present paper.
A Note on $(p,q)$-analogue Type of Frobenius-Genocchi Numbers and Polynomials
Waseem A. Khan,Idrees A. Khan 영남수학회 2020 East Asian mathematical journal Vol.36 No.1
The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and inves- tigate some basic identities and properties for these polynomials and num- bers including addition theorems, difference equations, derivative proper- ties, recurrence relations. We also obtain integral representations, im- plicit and explicit formulas and relations for these polynomials and num- bers. Furthermore, we consider some relationships for Apostol type (p, q)- Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.
ON HIGHER ORDER (p, q)-FROBENIUS-GENOCCHI NUMBERS AND POLYNOMIALS
Waseem A. Khan,Idrees A. Khan,J.Y. Kang 한국전산응용수학회 2019 Journal of applied mathematics & informatics Vol.37 No.3
In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.
ON HIGHER ORDER (p, q)-FROBENIUS-GENOCCHI NUMBERS AND POLYNOMIALS
KHAN, WASEEM A.,KHAN, IDREES A.,KANG, J.Y. The Korean Society for Computational and Applied M 2019 Journal of applied mathematics & informatics Vol.37 No.3
In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order ${\alpha}$ associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.
A NOTE ON (p, q)-ANALOGUE TYPE OF FROBENIUS-GENOCCHI NUMBERS AND POLYNOMIALS
Khan, Waseem A.,Khan, Idrees A. The Youngnam Mathematical Society 2020 East Asian mathematical journal Vol.36 No.1
The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations. We also obtain integral representations, implicit and explicit formulas and relations for these polynomials and numbers. Furthermore, we consider some relationships for Apostol type (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.