19 research outputs found
Extended Jacobi Functions via Riemann-Liouville Fractional Derivative
By means of the Riemann-Liouville fractional calculus, extended Jacobi functions are defined and some of their properties are obtained. Then, we compare some properties of the extended Jacobi functions extended Jacobi polynomials. Also, we derive fractional differential equation of generalized extended Jacobi functions
Parametric kinds of generalized Apostol-Bernoulli polynomials and their properties
The purpose of this paper is to define generalized Apostol--Bernoulli
polynomials with including a new cosine and sine parametric type of generating
function using the quasi-monomiality properties and trigonometric functions. In
this study, the Apostol-Bernoulli polynomials with three variable are defined
with two new generating functions cosine and sine parameters. Then, we
investigate multiplicative and derivative operators, diffrential equations,
some summation formulas and partial differential equations for these
polynomials. Moreover, we introduce Gould--Hopper--Apostol--Bernoulli type
polynomials, Hermite--Appell--Apostol--Bernoulli type polynomials and truncated
exponential Apostol--Bernoulli type polynomials. Finally, the special cases of
these new polynomials are investigated, and the corresponding results are
expressed.Comment: 16 page
Üç Değişkenli Fibonacci Tipli Polinomlar için Doğurucu Fonksiyonlar ve Bazı Özellikleri
Bu çalışmada ilk olarak iyi bilinen bazı polinom ailelerinin ve özel sayıların tanımlarına yer verilmiştir. Daha sonra Fibonacci tipli polinom ve sayı ailelerini içeren yeni doğurucu fonksiyonlar tanıtılmıştır. Bu polinom ailelerinin açık gösterimi ve doğurucu fonksiyonlarının kısmi türevleri ile bu ailelerin rekürans bağıntıları elde edilmiştir
Matrix Analogues of Some Properties for Bessel Matrix Functions
In this study, we obtain some recurrence relations for Bessel matrix functions of the first kind. Then we derive a new integral representation of these matrix functions. We lastly give new relations between Bessel matrix functions of the first kind and Laguerre matrix polynomials