Exponential rings, exponential polynomials and exponential functions

Generalized Exponential Euler Polynomials and Exponential Splines

Here presented is constructive generalization of exponential Euler polynomial and exponential splines based on the interrelationship between the set of concepts of Eulerian polynomials, Eulerian numbers, and Eulerian fractions and the set of concepts related to spline functions. The applications of generalized exponential Euler polynomials in series transformations and expansions are also given.

Limit summability of ultra exponential functions

In [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.Also, we exhibited the topic of limit summability of real functions in [2,3]. Inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. Finally, we pose an unsolved problem aboutthem.

Exponential polynomials and D-modules

We introduce D-modules adapted to study ideals generated by exponential polynomials. ∗Partially supported by the NSF grants DMS-9000619 and CDR-8803012 †Partially supported by the NSF grant DMS-9000619

Exponential Transforms and Appell Polynomials.

limit summability of ultra exponential functions

in [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.also, we exhibited the topic of limit summability of real functions in [2,3]. inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. finally, we pose an unsolved problem aboutthem.