scholarly journals SOME RECURRENCE FORMULAS FOR A NEW CLASS OF SPECIAL POLYNOMIALS AND SPECIAL FUNCTIONS

2020 ◽  
Vol 14 (1) ◽  
Author(s):  
Snježana Maksimović ◽  
Nebojša Đurić ◽  
Ivan Vanja Boroja ◽  
Sandra Kosić-Jeremić
Keyword(s):  
Differential Equations ◽  
Special Functions ◽  
Second Order ◽  
Real Numbers ◽  
New Class ◽  
Recurrence Formulas ◽  
Special Polynomials ◽  
Summation Formulas ◽  
Integrable Functions ◽  
Square Integrable Functions

In this paper we used a new class of special functions and special polynomials which are solutions different Sturm Liouvile differential equations of second order. These functions form a basis of a space of square integrable functions over set of a real numbers. We investigated some properties of these polynomials and established some recurrence formulas. Using a new class of special functions, we obtained some useful summation formulas and recurrence formulas.

scholarly journals Fixed point theorems via Generalized WF-Contractions with applications

SeMA Journal ◽  
2021 ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Rakesh Tiwari
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
New Class ◽  
Second Order Differential Equations ◽  
Fixed Point Result

AbstractThe aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

scholarly journals Fisher information of special functions and second-order differential equations

2008 ◽  
Vol 49 (8) ◽  
pp. 082104 ◽  
Author(s):  
R. J. Yáñez ◽  
P. Sánchez-Moreno ◽  
A. Zarzo ◽  
J. S. Dehesa
Keyword(s):  
Differential Equations ◽  
Fisher Information ◽  
Special Functions ◽  
Second Order ◽  
Second Order Differential Equations

scholarly journals On a method for constructing Bergman kernels

1980 ◽  
Vol 29 (4) ◽  
pp. 454-461
Author(s):  
A. Azzam ◽  
E. Kreyszig
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Second Order ◽  
Partial Differential ◽  
Bergman Kernels ◽  
Order Linear ◽  
Independent Variables ◽  
New Class ◽  
Linear Partial Differential Equations ◽  
Two Independent Variables

AbstractWe establish a method of constructing kernels of Bergman operators for second-order linear partial differential equations in two independent variables, and use the method for obtaining a new class of Bergman kernels, which we call modified class E kernels since they include certain class E kernals. They also include other kernels which are suitable for global representations of solutions (whereas Bergman operators generally yield only local representations).

scholarly journals On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials

2006 ◽  
Vol 58 (4) ◽  
pp. 726-767 ◽  
Author(s):  
Yik-Man Chiang ◽  
Mourad E. H. Ismail
Keyword(s):  
Differential Equations ◽  
Special Functions ◽  
Complete Characterization ◽  
Second Order ◽  
Value Distribution ◽  
Value Distribution Theory ◽  
Confluent Hypergeometric Functions ◽  
Number Of Zeros ◽  
Oscillation Of Solutions

AbstractWe show that the value distribution (complex oscillation) of solutions of certain periodic second order ordinary differential equations studied by Bank, Laine and Langley is closely related to confluent hypergeometric functions, Bessel functions and Bessel polynomials. As a result, we give a complete characterization of the zero-distribution in the sense of Nevanlinna theory of the solutions for two classes of the ODEs. Our approach uses special functions and their asymptotics. New results concerning finiteness of the number of zeros (finite-zeros) problem of Bessel and Coulomb wave functions with respect to the parameters are also obtained as a consequence. We demonstrate that the problem for the remaining class of ODEs not covered by the above “special function approach” can be described by a classical Heine problem for differential equations that admit polynomial solutions.

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