Theory of Linear Hahn difference equations
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2013, Vol 4, Issue 2
Abstract
Hahn introduced the dierence operator Dq,wf (t)=(f(qt+w)-f(t))/(t(q-1)+w) in 1949, where 0<q<1 and w>0 are fixed real numbers. This operator extends the classical differance operator Vwf(t) = (f(t + w)-f(t))/w as well as Jackson q- dierence operator Dqf(t) = (f(qt)-f(t))/(t(q-1)). In this paper, our target is to give a rigorous study of the theory of linear Hahn dierence equations of the form a0(t)Dnq,wX(t) + a1(t)Dn-1q,w x(t) + ...+ an(t)x(t) = 0: We introduce its fundamental set of solutions when the coefficients are constant and the Wronskian associated with Dq,w. Hence, we obtain the corresponding Liouville's formula. Also, we derive solutions of the first and second order linear Hahn dierence equations with non-constant coffiecients. Finally, we present the analogues of the variation of parameter technique and the annihilator method for the non-homogeneous case.
Authors and Affiliations
Alaa E. Hamza, S. M. Ahmed
Keywords
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- EP ID EP651240
- DOI 10.24297/jam.v4i2.2496
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