Limiting Values and Functional and Difference Equations

Abstract

Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results. This involves the expression for the Laurent coefficients including the residue, the Kronecker limit formulas and higher order coefficients as well as the difference formed to cancel the inaccessible part, typically the Clausen functions. We also state Abelian results which yield asymptotic formulas for weighted summatory function from that for the original summatory function.This clarifies the second equality in (62). For a general form, cf. (98).Comtet [19, pp. 224-229] is the most informative reference book on Stirling numbers.Preprints (www.preprints.org) | NOT PEER-REVIEWED |

High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation

“…Alderremy et al structured new models of the multi-space fractional Gardner equation [3]. Wang et al considered some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results [41]. El-Sayed et al introduced a numerical technique for solving a class of multi-term variable-order fractional differential equations [11].…”