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Integral Transforms and Special Functions Volume 32, 2021 - Issue 11
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Research Articles

On the properties of zeros of Bessel series in the real line

Antonio J. Durána Departamento de Análisis Matemático and IMUS, Universidad de Sevilla, Sevilla, SpainORCID Iconhttps://orcid.org/0000-0002-8351-7392View further author information
ORCID Icon,
Mario Pérezb Departamento de Matemáticas and IUMA, Universidad de Zaragoza, Zaragoza, SpainView further author information
&
Juan L. Varonac Departamento de Matemáticas y Computación, Universidad de La Rioja, Logroño, SpainCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-2023-9946View further author information
ORCID Icon
Pages 912-931 | Received 08 Jul 2020, Accepted 15 Dec 2020, Published online: 31 Dec 2020

References

  • Watson GN. A treatise on the theory of Bessel functions. Cambridge: Cambridge University Press; 1944.
  • Szegö G. Orthogonal polynomials. 4th ed. Providence (RI): American Mathematical Society; 1975.
  • Temme NM. Numerical methods. In: NIST handbook of mathematical functions. NIST and Cambridge University Press; 2010. p. 71–101. Available from: http://dlmf.nist.gov/3.
  • Driver K, Jordaan K, Martínez-Finkelshtein A. Pólya frequency sequences and real zeros of some 3F2 polynomials. J Math Anal Appl. 2007;332(2):1045–1055.
  • Marcellán F, Rafaeli FR. A note on monotonicity of zeros of generalized Hermite-Sobolev-type orthogonal polynomials. Integral Transforms Spec Funct. 2010;21(11):831–838.
  • Cerone P. Series involving zeros of transcendental functions including zeta. Integral Transforms Spec Funct. 2012;23(10):709–718.
  • Jordaan K, Wang H, Zhou J. Monotonicity of zeros of polynomials orthogonal with respect to an even weight function. Integral Transforms Spec Funct. 2014;25(9):721–729.
  • Durán AJ, Pérez M, Varona JL. Some conjectures on Wronskian and Casorati determinants of orthogonal polynomials. Exp Math. 2015;24(1):123–132.
  • Driver K, Muldoon ME. Zeros of quasi-orthogonal ultraspherical polynomials. Indag Math (NS). 2016;27(4):930–944.
  • Olver FWJ, Maximon LC. Bessel functions. In: NIST handbook of mathematical functions. NIST and Cambridge University Press; 2010. p. 215–286. Available from: http://dlmf.nist.gov/10.
  • Gil A, Segura J. A combined symbolic and numerical algorithm for the computation of zeros of orthogonal polynomials and special functions. J Symbolic Comput. 2003;35(5):465–485.
  • Ciaurri Ó, Durán AJ, Pérez M, et al. Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions. J Approx Theory. 2018;235:20–45.
  • Durán AJ, Pérez M, Varona JL. Fourier-Dunkl system of the second kind and Euler-Dunkl polynomials. J Approx Theory. 2019;245:23–39.
  • Ciaurri Ó, Mínguez Ceniceros J, Varona JL. Bernoulli-Dunkl and Euler-Dunkl polynomials and their generalizations. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM. 2019;113(3):2853–2876.
  • Rawn MD. On the summation of Fourier and Bessel series. J Math Anal Appl. 1995;193(1):282–295.
  • Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and series, Vol. 2: special functions. New York: Gordon and Breach; 1988.

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