On the q-extension of Euler and Genocchi numbers
By Taekyun Kim. 2007
180 citations recorded by the source corpus.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/5228fde2eee5e175cc5ac9d76da048f7ca066d58
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Taekyun Kim
- Yilmaz Simsek
- Hari M. Srivastava
- Burak Kurt
- I. N. Cangul
- Hacer Ozden
- Seog-Hoon Rim
- Qiu-Ming Luo
In Discrete Mathematics and Combinatorics
- Yilmaz Simsek
- Taekyun Kim
- Hari M. Srivastava
- I. N. Cangul
- Hacer Ozden
- Seog-Hoon Rim
- Burak Kurt
- Veli Kurt
Citations in the corpus
- On the multiple q-Genocchi and Euler numbers (2008, background): “Hence, limq→1[x]q = 1, for any x with |x|p ≤ 1 in the present p-adic case, cf.[1-18].”
- New approach to q-Euler polynomials of higher order (2010, unknown): “lx (1+ ql+1) . In the special case x = 0, En,q(= En,q(0)) are called the n-th q-Euler numbers. From (3), we can easily derive the following relation. E0,q = 1, and q(qE + 1)n +En,q = 0 if n ≥ 1, (see [8, 16, 17]), 2 where we use the standard convention about replacing Ek by Ek,q. It is easy to show ”
- A note on p-adic q-Euler measure (2007, methodology): “In the recent paper [3], the q-extension of Euler numbers are defined inductively by”
- Some families of Genocchi type polynomials and their interpolation functions (2012, background): “ction (sometimes called the Hurwitz-Lerch zeta function) L(λ,α,s) = Φ(e2πiλ,s,α), 11 which is a special function and generalizes the Hurwitz zeta function and polylogarithm, cf. ([2], [31], [4], [6], [7], [9], [8], [12], [17], [27]) and see also the references cited in each of these earlier works. S”
- Complete sum of products of (h, q)-extension of Euler polynomials and numbers (2010, methodology): “I1 (f) = lim q!1Iq (f), cf. ([7], [10], [ 11 ], , [17]).”
- The Modified q-Euler numbers and polynomials (2007, background): “In the recent paper (see [6]) we defined a set of numbers inductively by E0,q = 1, q(qE + 1) n +En,q = (”