58 citations · 68 across the 5 of their papers we have counts for
7 papers
Double q-Analytic q-Hermite Binomial Formula and q-Traveling Waves
Sengul Nalci, Oktay K. Pashaev
Motivated by derivation of the Dirac type delta-function for quantum states in Fock-Bargmann representation, we find q-binomial expansion in terms of q-Hermite polynomials, analyti…
q-Bernoulli Numbers and Zeros of q-Sine Function
Sengul Nalci, Oktay Pashaev
There exists a well-known relation between the zeros of sine function, Bernoulli numbers and the Riemann Zeta function. In the present paper, we find a similar relation for zeros o…
Non-Commutative Q-Binomial Formula
Sengul Nalci, Oktay Pashaev
In this paper, we found new q-binomial formula for Q-commutative operators. Expansion coefficients in this formula are given by q-binomial coefficients with two bases (q,Q), determ…
Golden Quantum Oscillator and Binet-Fibonacci Calculus
Oktay K. Pashaev, Sengul Nalci
The Binet-Fibonacci formula for Fibonacci numbers is treated as a q-number (and q-operator) with Golden ratio bases and . Quantum harmonic oscillator for this Golden…
q-damped Oscillator and degenerate roots of constant coefficients q-difference ODE
Sengul Nalci, Oktay K. Pashaev
The classical model of q-damped oscillator is introduced and solved in terms of Jackson q-exponential function for three different cases, under-damped, over-damped and the critical…
q-Shock Soliton Evolution
Oktay K. Pashaev, Sengul Nalci
By generating function based on the Jackson's q-exponential function and standard exponential function, we introduce a new q-analogue of Hermite and Kampe-de Feriet polynomials. In…