Kokologiannaki, Chrysi G.; Laforgia, Andrea Simple proofs of classical results on zeros of \(J_{\nu}(x)\) and \(J'_{\nu}(x)\). (English) Zbl 1305.33008 Tbil. Math. J. 7, No. 2, 35-39 (2014). Summary: The Bessel functions \(J_{\nu}(x)\) and their derivatives \(J'_{\nu}(x)\) can be represented by infinite series and infinite products. Using these representations we give very simple proofs for known results concerning the zeros of the above functions. Cited in 1 Document MSC: 33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\) Keywords:Bessel functions; derivative of Bessel functions; zeros; Rayleigh sums Software:DLMF PDF BibTeX XML Cite \textit{C. G. Kokologiannaki} and \textit{A. Laforgia}, Tbil. Math. J. 7, No. 2, 35--39 (2014; Zbl 1305.33008) Full Text: DOI OpenURL References: [1] [1] D.P.Gupta and M.E.Muldoon, Riccati equations and convolution formulae for functions of Rayleigh type, J.Phys. A: Math.Gen.33 (2000) 1363-1368. · Zbl 0953.33003 [2] N.Kishore, The Rayleigh function, Proc. of Amer. Math. soc. 14, 4 (1963), 527-533. · Zbl 0117.29904 [3] M.E.Muldoon and A.Raza, Convolution formulae for functions of Rayleigh type, J.Phys. A: Math. Gen. 31 (1998) 9327-9330. · Zbl 0937.33005 [4] F.Olver, D.Lozier, R. Boisvert, C.Clark, NIST handbook of MAthematical functions, Cambrigde University Press (2010) · Zbl 1198.00002 [5] G.N.Watson, A treatise on the theory of Bessel functions, Cambridge University Press (1966). · Zbl 0174.36202 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.