Simple proofs of classical results on zeros of \(J_{\nu}(x)\) and \(J'_{\nu}(x)\). (English) Zbl 1305.33008

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.


33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)


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[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
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