Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1709731 | Applied Mathematics Letters | 2010 | 5 Pages |
Abstract
In a recent paper [M. Masjed-Jamei, H.M. Srivastava, An integral expansion for analytic functions based upon the remainder values of the Taylor series expansions, Appl. Math. Lett. 22 (2009) 406–411], a new type of integral expansions for analytic functions was introduced and investigated. In this sequel to our earlier paper, we make use of the aforementioned expansion in order to explicitly obtain the general solutions of the following functional equation: f(k+1)(a)+bkf(k)(a)=ckf(k+1)(a)+bkf(k)(a)=ck(k∈N0≔N∪{0};N≔{1,2,3,⋯}) for various kinds of real sequences {bk}{bk} and {ck}{ck}, where (as usual) f(k)(a)f(k)(a) is the kkth derivative of the unknown function f(x)f(x) at x=ax=a. We also present some illustrative examples in this sense.
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Mohammad Masjed-Jamei, H.M. Srivastava,