Functional equations with distortion and certain q-special functions

2000 ◽  
Vol 59 (1) ◽  
pp. 38-44 ◽  
Author(s):  
R. L. Rubin
Keyword(s):  
Functional Equations ◽  
Special Functions

scholarly journals Limiting Values and Functional and Difference Equations

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 407 ◽  
Author(s):  
N.-L. Wang ◽  
Praveen Agarwal ◽  
S. Kanemitsu
Keyword(s):  
Difference Equations ◽  
Functional Equations ◽  
Boundary Behavior ◽  
Special Functions ◽  
Asymptotic Formulas ◽  
Limit Values ◽  
Summatory Function ◽  
The Difference ◽  
Limiting Values ◽  
Mathematics And Science

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. As main 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 establish these by the relation between bases of the Kubert space of functions. Then these expressions are equated with other expressions in terms of special functions introduced by some difference equations, giving rise to analogues of the Lerch-Chowla-Selberg formula. We also state Abelian results which not only yield asymptotic formulas for weighted summatory function from that for the original summatory function but assures the existence of the limit expression for Laurent coefficients.

scholarly journals Special functions and the Mellin transforms of Laguerre and Hermite functions

Analysis ◽  
2007 ◽  
Vol 27 (1) ◽  
Author(s):  
Mark W. Coffey
Keyword(s):  
Functional Equations ◽  
Hypergeometric Functions ◽  
Critical Line ◽  
Special Functions ◽  
Hermite Functions ◽  
Mellin Transforms ◽  
Reciprocity Laws ◽  
Explicit Expressions

We present explicit expressions for the Mellin transforms of Laguerre and Hermite functions in terms of a variety of special functions. We show that many of the properties of the resulting functions, including functional equations and reciprocity laws, are direct consequences of transformation formulae of hypergeometric functions. Interest in these results is reinforced by the fact that polynomial or other factors of the Mellin transforms have zeros only on the critical line Re

scholarly journals A survey on the stability of mean value points and functional equations involving some special functions

2015 ◽  
Vol 24 (1) ◽  
pp. 27-42
Author(s):  
SORINEL DUMITRESCU ◽  
◽  
MIHAI MONEA ◽  
CRISTINEL MORTICI ◽  
◽  
...  
Keyword(s):  
Functional Equations ◽  
Special Functions ◽  
Mean Value ◽  
Mean Value Theorems ◽  
The Stability

The aim of this work is to put together some of the recent and classical results in the theory of stability. In the first part, we recall the results regarding the intermediary points arising from various Mean Value Theorems, then we study the stability of some functional equations involving the gamma and beta functions.

On some functional equations related to derivations and bicircular projections in rings

2014 ◽  
Vol 49 (2) ◽  
pp. 313-331
Author(s):  
Maja Fošner ◽  
◽  
Benjamin Marcen ◽  
Nejc Širovnik ◽  
Joso Vukman ◽  
...  
Keyword(s):  
Functional Equations

Functional equations related to weightable quasi-metrics

2015 ◽  
Vol 4 (1047) ◽  
Author(s):  
M.J. Campion ◽  
E. Indurain ◽  
G. Ochoa
Keyword(s):  
Functional Equations

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

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