The complete monotonicity of the Rayleigh function

Obi, Eguono

doi:10.1016/0022-247x(80)90240-1

Cited by 4 publications

(3 citation statements)

References 8 publications

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“…532]. We also note here that in particular when η = 0 the results of Theorem 4 reduce to the main results of Obi [Ob,p. 466] concerning the complete monotonicity of the functions ν → σ 2q (ν), ν → (ν + 1) q σ 2q (ν) and (ν + q)σ 2q (ν) on (−1/2, ∞), where q ∈ {1, 2, .…”

Section: á Bariczsupporting

confidence: 62%

Turán type inequalities for regular Coulomb wave functions

Baricz

2015

Journal of Mathematical Analysis and Applications

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Section: á Bariczsupporting

confidence: 62%

Turán type inequalities for regular Coulomb wave functions

Baricz

2015

Journal of Mathematical Analysis and Applications

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“…] for details; various ramifications were considered recently in [2]), we can find all the σ n (ν) in terms of the coefficients in the series (2). If we want to deal (as in [3]) with properties of the σ n (ν) as functions of ν, there is a useful compact convolution formula due to Kishore [4] σ n (ν)…”

Section: Introductionmentioning

confidence: 99%

Riccati equations and convolution formulae for functions of Rayleigh type

Gupta

Muldoon

2000

J. Phys. A: Math. Gen.

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N. Kishore, Proc. Amer. Math. Soc. 14 527 (1963), considered the Rayleigh functions σ n (ν) = ∞ k=1 j −2n νk , n = 1, 2, . . ., where ±j νk are the (non-zero) zeros of the Bessel function J ν (z) and provided a convolution type sum formula for finding σ n in terms of σ 1 , . . . , σ n−1 . His main tool was the recurrence relation for Bessel functions. Here we extend this result to a larger class of functions by using Riccati differential equations. We get new results for the zeros of certain combinations of Bessel functions and their first and second derivatives as well as recovering some results of Buchholz for zeros of confluent hypergeometric functions.

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“…Formula 6is useful in proving higher monotonicity properties of the Rayleigh functions [4] and in deriving congruence properties for some of their functional values [5].…”

mentioning

confidence: 99%

Convolution formulae for functions of Rayleigh type

Muldoon¹,

Raza²

1998

J. Phys. A: Math. Gen.

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N. Kishore, Proc. Amer. Math. Soc. 14 527 (1963), considered the Rayleigh functions σ n (ν) = ∞ k=1 j −2n νk , n = 1, 2,. . ., where the j νk are the (non-zero) zeros of the Bessel function J ν (z) and has provided a convolution type sum formula for finding σ n in terms of σ 1 ,. .. , σ n−1. Here we investigate corresponding expressions for sums of reciprocal powers of zeros τ n of derivatives and other functions related to Bessel functions. It turns out that we can get results similar to Kishore's expressing τ n in terms of τ 1 ,. .. , τ n−1 and σ 1 ,. .. , σ n .

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The complete monotonicity of the Rayleigh function

Cited by 4 publications

References 8 publications

Turán type inequalities for regular Coulomb wave functions

Turán type inequalities for regular Coulomb wave functions

Riccati equations and convolution formulae for functions of Rayleigh type

Convolution formulae for functions of Rayleigh type

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