scholarly journals Asymptotics of derivatives of orthogonal polynomials on the real line

2007 ◽  
Vol 118 (1-2) ◽  
pp. 115-127
Author(s):  
E. Levin ◽  
D. S. Lubinsky
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
The Real ◽  
Derivatives Of

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

scholarly journals Sylvester equations for Laguerre–Hahn orthogonal polynomials on the real line

2013 ◽  
Vol 219 (17) ◽  
pp. 9118-9131 ◽  
Author(s):  
A. Branquinho ◽  
A. Paiva ◽  
M.N. Rebocho
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
The Real

scholarly journals Some remarks on incomplete gamma type function γ*(α, x_)

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 125-131 ◽  
Author(s):  
Emin Özcağ ◽  
İnci Egeb
Keyword(s):  
Recurrence Relation ◽  
Real Line ◽  
Summable Function ◽  
Type Function ◽  
The Real ◽  
Definition Of ◽  
Derivatives Of

The incomplete gamma type function ?*(?, x_) is defined as locally summable function on the real line for ?>0 by ?*(?,x_) = {?x0 |u|?-1 e-u du, x?0; 0, x > 0 = ?-x_0 |u|?-1 e-u du the integral divergining ? ? 0 and by using the recurrence relation ?*(? + 1,x_) = -??*(?,x_) - x?_ e-x the definition of ?*(?, x_) can be extended to the negative non-integer values of ?. Recently the authors [8] defined ?*(-m, x_) for m = 0, 1, 2,... . In this paper we define the derivatives of the incomplete gamma type function ?*(?, x_) as a distribution for all ? < 0.

scholarly journals LOWERING AND RAISING OPERATORS FOR THE FREE MEIXNER CLASS OF ORTHOGONAL POLYNOMIALS

2009 ◽  
Vol 12 (03) ◽  
pp. 387-399 ◽  
Author(s):  
EUGENE LYTVYNOV ◽  
IRINA RODIONOVA
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
Meixner Polynomials ◽  
The Real ◽  
Raising Operators ◽  
Meixner Class

We compare some properties of the lowering and raising operators for the classical and free classes of Meixner polynomials on the real line.

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