کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772652 | 1630633 | 2017 | 31 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials
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کلمات کلیدی
34A9935A99Humbert polynomials11M3526C0511B8311B6805A1533C0505A1026C1011B3711B39primary - اولیهStirling numbers of the first kind - تعداد استرلینگ از نوع اولLucas numbers - تعداد لوکاسHypergeometric functions - توابع هیپرگومتریکGenerating functions - تولید توابعsecondary - ثانویCauchy numbers - شماره کوشیBinomial coefficients - ضرایب دوجمله ایPartial differential equations - معادلات دیفرانسیل جزئیFunctional equations - معادلات کاربردی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The main motivation of this paper is to investigate some derivative properties of the generating functions for the numbers Yn(λ) and the polynomials Yn(x;λ), which were recently introduced by Simsek [30]. We give functional equations and differential equations (PDEs) of these generating functions. By using these functional and differential equations, we derive not only recurrence relations, but also several other identities and relations for these numbers and polynomials. Our identities include the Apostol-Bernoulli numbers, the Apostol-Euler numbers, the Stirling numbers of the first kind, the Cauchy numbers and the Hurwitz-Lerch zeta functions. Moreover, we give hypergeometric function representation for an integral involving these numbers and polynomials. Finally, we give infinite series representations of the numbers Yn(λ), the Changhee numbers, the Daehee numbers, the Lucas numbers and the Humbert polynomials.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 181, December 2017, Pages 117-146
Journal: Journal of Number Theory - Volume 181, December 2017, Pages 117-146
نویسندگان
H.M. Srivastava, Irem KucukoÄlu, Yilmaz Simsek,