scholarly journals A Neumann series of Bessel functions representation for solutions of Sturm–Liouville equations

CALCOLO ◽  
2018 ◽  
Vol 55 (1) ◽  
Author(s):  
Vladislav V. Kravchenko ◽  
Sergii M. Torba
Keyword(s):  
Bessel Functions ◽  
Neumann Series ◽  
Sturm Liouville

Rational approximation to Neumann series of Bessel functions

1992 ◽  
Vol 3 (1) ◽  
pp. 235-244 ◽  
Author(s):  
N. Hayek ◽  
P. González-Vera ◽  
F. Pérez-Acosta
Keyword(s):  
Rational Approximation ◽  
Bessel Functions ◽  
Neumann Series

scholarly journals q-Titchmarsh-Weyl theory: series expansion

2012 ◽  
Vol 205 ◽  
pp. 67-118
Author(s):  
M. H. Annaby ◽  
Z. S. Mansour ◽  
I. A. Soliman
Keyword(s):  
Limit Point ◽  
Eigenfunction Expansion ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Limit Circle ◽  
Worked Example ◽  
Weyl Theory ◽  
Sturm Liouville ◽  
Limit Point Case ◽  
Theory Series

AbstractWe establish aq-Titchmarsh-Weyl theory for singularq-Sturm-Liouville problems. We defineq-limit-point andq-limit circle singularities, and we give sufficient conditions which guarantee that the singular point is in a limit-point case. The resolvent is constructed in terms of Green’s function of the problem. We derive the eigenfunction expansion in its series form. A detailed worked example involving Jacksonq-Bessel functions is given. This example leads to the completeness of a wide class ofq-cylindrical functions.

Neumann series of Bessel functions

2012 ◽  
Vol 23 (7) ◽  
pp. 529-538 ◽  
Author(s):  
Árpád Baricz ◽  
Dragana Jankov ◽  
Tibor K. Pogány
Keyword(s):  
Bessel Functions ◽  
Neumann Series

scholarly journals A Neumann series of Bessel functions representation for solutions of perturbed Bessel equations

2017 ◽  
Vol 97 (5) ◽  
pp. 677-704 ◽  
Author(s):  
Vladislav V. Kravchenko ◽  
Sergii M. Torba ◽  
Raúl Castillo-Pérez
Keyword(s):  
Bessel Functions ◽  
Neumann Series

scholarly journals q-Titchmarsh-Weyl theory: series expansion

2012 ◽  
Vol 205 ◽  
pp. 67-118 ◽  
Author(s):  
M. H. Annaby ◽  
Z. S. Mansour ◽  
I. A. Soliman
Keyword(s):  
Limit Point ◽  
Eigenfunction Expansion ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Limit Circle ◽  
Worked Example ◽  
Weyl Theory ◽  
Sturm Liouville ◽  
Limit Point Case ◽  
Theory Series

AbstractWe establish a q-Titchmarsh-Weyl theory for singular q-Sturm-Liouville problems. We define q-limit-point and q-limit circle singularities, and we give sufficient conditions which guarantee that the singular point is in a limit-point case. The resolvent is constructed in terms of Green’s function of the problem. We derive the eigenfunction expansion in its series form. A detailed worked example involving Jackson q-Bessel functions is given. This example leads to the completeness of a wide class of q-cylindrical functions.

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