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An interesting new result involving associated laguerre polynomials
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An interesting new integral expression involving two Associated Laguerre Polynomials is derived, and seven special cases of this expression are discussed.Abstract:
An interesting new integral expression involving two Associated Laguerre Polynomials is derived, and seven special cases of this expression are discussed.read more
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Remarks on some associated Laguerre integral results
TL;DR: The main object of the present sequel to these recent works is to investigate and apply much more general families of integral formulas, involving products of two or more Laguerre polynomials, which have been considered in the mathematical literature rather extensively.
Journal ArticleDOI
Some Integrals of the products of laguerre polynomials
TL;DR: The present sequel to these earlier works is to consider a family of such integrals of the products of Laguerre, Hermite, and other classical orthogonal polynomials in a systematic and unified manner.
Journal ArticleDOI
Radial position–momentum uncertainties for the Dirac hydrogen-like atoms
Wen Chao Qiang,Shi-Hai Dong +1 more
TL;DR: In this paper, the radial position-momentum uncertainty product for Dirac hydrogen-like atoms was analyzed analytically for the same principal quantum number n and the azimuthal quantum number l. The relativistic corrections to the non-relativistic values of uncertainties are very small when the values of charge Z are not too big.
Journal ArticleDOI
Two new associated Laguerre integral results
TL;DR: The expression used to obtain new associated Laguerre integral results is compared to that given in [2] and shown to be different and of greater generality and some physical moments are discussed that require such integrals.
Journal ArticleDOI
Quantum features in the orthogonality of optical modes for structured and plane-wave light
David L. Andrews,Kayn A. Forbes +1 more
TL;DR: A suitable reformulation of the relationship between operator commutation and mode orthogonality has special relevance to optical vortex physics-particularly with regard to information content-through its connection to the degrees of freedom in the associated radiation modes.
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Quantum mechanics
TL;DR: The blackbody radiation problem was solved by Max Planck as mentioned in this paper, who showed that radiation was not continuous but discrete, coming in lumps known as quanta, which became known as Planck's constant and led to the correct prediction of the blackbody spectrum.