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Ars Combinatoria

  • Research article

On a \(p\)-Adic Interpolating Function for the Generalized Genocchi Numbers and Its Behaviour at \(s=0\)

Serkan Araci1, Erdogan Sen2
1DEPARTMENT OF ECONOMICS, FACULTY OF ECONOMICS, ADMINISTRATIVE AND SOCIAL SCIENCE, HASAN KALYONCU UNIVERSITY, TR-27410 GAZIANTEP, TURKEY
2DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE AND LETTERS, NAMIK KEMAL UNIVERSITY, 59030 TekirnpaG, TURKEY; DEPARTMENT OF MATHE- MATICS ENGINEERING, ISTANBUL TECHNICAL UNIVERSITY, MASLAK, 34469 Is- TANBUL, TURKEY
  • Published: 31/07/2015

Abstract

In this work, we consider the generalized Genocchi numbers and polynomials. However, we introduce an analytic interpolating function for the generalized Genocchi numbers attached to \(\chi\) at negative integers in the complex plane, and also we define the Genocchi \(p\)-adic \(L\)-function. As a result, we derive the value of the partial derivative of the Genocchi \(p\)-adic \(l\)-function at \(s = 0\).

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Citation
Serkan Araci, Erdogan Sen. On a \(p\)-Adic Interpolating Function for the Generalized Genocchi Numbers and Its Behaviour at \(s=0\)[J], Ars Combinatoria, Volume 122. 439-447. .