Preprint Article Version 1 This version is not peer-reviewed

Limiting Values and Functional and Difference Equations

Version 1 : Received: 16 February 2020 / Approved: 17 February 2020 / Online: 17 February 2020 (15:10:08 CET)

A peer-reviewed article of this Preprint also exists.

Wang, N.-L.; Agarwal, P.; Kanemitsu, S. Limiting Values and Functional and Difference Equations. Mathematics 2020, 8, 407. Wang, N.-L.; Agarwal, P.; Kanemitsu, S. Limiting Values and Functional and Difference Equations. Mathematics 2020, 8, 407.

Journal reference: Mathematics 2020, 8, 407
DOI: 10.3390/math8030407

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

Subject Areas

limit values; modular relation; Lerch zeta-function; Hurwitz zetafunction; Laurent coefficients

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