publication . Preprint . Other literature type . Article . 2015

Turán type inequalities for regular Coulomb wave functions

Árpád Baricz;
Open Access English
  • Published: 01 Oct 2015
Abstract
Comment: 11 pages
Subjects
arXiv: Mathematics::Classical Analysis and ODEsCondensed Matter::Mesoscopic Systems and Quantum Hall EffectMathematics::Probability
free text keywords: Mathematics - Classical Analysis and ODEs, 33C15, Applied Mathematics, Analysis, Interlacing, Wave function, Mathematics, Coulomb, Coulomb wave function, Mathematical analysis, Mathematical proof, Monotonic function
22 references, page 1 of 2

L + 1 if η = 0 [AS] M. Abramowitz, I.A. Stegun (Eds.), Handbook of Mathematical Functions with formulas. Graphs and Mathematical Tables, Dover Publications, New York, 1965.

[Ba] A´ . Baricz, Functional inequalities involving Bessel and modified Bessel functions of the first kind, Expo. Math. 26 (2008) 279-293. [OpenAIRE]

[BP] A´ . Baricz, T.K. Poga´ny, Tura´n determinants of Bessel functions, Forum Math. 26 (2014) 295-322.

[BS] A´ . Baricz, J. Sa´ndor, Extensions of the generalized Wilker inequality to Bessel functions, J. Math. Inequal. 2(3) (2008) 397-406.

[BI] J. Bustoz, M.E.H. Ismail, Tura´n inequalities for symmetric orthogonal polynomials, Internat. J. Math. Math. Sci. 20 (1997) 1-8.

[Ik] Y. Ikebe, The zeros of regular Coulomb wave functions and of their derivatives, Math. Comp. 29(131) (1975) 878-887. [OpenAIRE]

[JB] C.M. Joshi, S.K. Bissu, Some inequalities of Bessel and modified Bessel functions, J. Austral. Math. Soc. (Series A) 50 (1991) 333-342.

[KS] S. Karlin, G. Szego˝, On certain determinants whose elements are orthogonal polynomials, J. Analyse Math. 8 (1960/61), 1-157.

[Ki] N. Kishore, The Rayleigh function, Proc. Amer. Math. Soc. 14 (1963) 527-533. [OpenAIRE]

[La] S.K. Lakshmana Rao, On the relative extrema of the Tura´n expression fo Bessel functions, Proc. Indian Acad. Sci. Sect. A 53 (1961) 239-243. [OpenAIRE]

[MKCI] Y. Miyazaki, Y. Kikuchi, D. Cai, Y. Ikebe, Error analysis for the computation of zeros of regular Coulomb wave function and its first derivative, Math. Comp. 70(235) (2001) 1195-1204.

[Ni] T. Nishiyama, Application of Coulomb wave functions to an orthogonal series associated with steady axisymmetric Euler flows, J. Approx. Theory 151 (2008) 42-59.

[Ob] E.C. Obi, The complete monotonicity of the Rayleigh function, J. Math. Anal. Appl. 77 (1980) 465-468. [OpenAIRE]

[Pa] M.L. Patrick, Extensions of inequalities of the Laguerre and Tura´n type, Pacific J. Math. 44 (1973) 675-682.

[Ro] D.K. Ross, Inequalities and identities for yn2 − yn−1yn+1, Aequat. Math. 20 (1980) 23-32.

22 references, page 1 of 2
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publication . Preprint . Other literature type . Article . 2015

Turán type inequalities for regular Coulomb wave functions

Árpád Baricz;