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The imaginary zeros of a mixed Bessel function

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Abstract

In the present work we study the existence and monotonicity properties of the imaginary zeros of the mixed Bessel functionM v(z)=(βz2+α)Jv(z)+zJ′v(z). Such a function includes as particular cases the functionsJ′ v(z)(α=β=0), J″v(z)(α=−v2,β=1)x andH v(z)=αJv(z)+zJ′v(z), whereJ v(z) is the Bessel function of the first kind and of orderv>−1 andJ′ v(z), J″v(z) are the first two derivatives ofJ v(z). Upper and lower bounds found for the imaginary zeros of the functionsJ′ v(z), J″v(z) andH v(z) improve previously known bounds.

Zusammenfassung

Dieser Artikel betrifft die Existenz und Monotonie von Eigenschaften imaginärer Nullen der gemischten BesselfunktionM v(z)=(βz2+α)Jv(z)+zJ′v(z). Eine solche Funktion enthält als Spezialfall die FunktionenJ′ v(z)(α=β=0), J″v(z)(α=−v2,β=1) undH v(z)=αJv(z)+zJ′v(z), woJ v(z)die Besselfunktion von erster Art und Ordnungv>−1 andJ′ v(z), J″v(z) sind die erste und zweite Ableitung vonJ v(z). Untere und obere Schranken, die für die imaginären Nullen der FunktionenJ′ v(z), J″v(z) undH v(z) gefunden wurden, verbessern früher bekannte Resultate.

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Authors and Affiliations

  1. Dept. of Mathematics, University of Patras, Greece

    E. K. Ifantis & P. D. Siafarikas

  2. National Research Center for Physical Sciences “Demokritos”, Aghia Paraskevi Attikis, Athens, Greece

    C. B. Kouris

Authors
  1. E. K. Ifantis
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  2. P. D. Siafarikas
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  3. C. B. Kouris
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Ifantis, E.K., Siafarikas, P.D. & Kouris, C.B. The imaginary zeros of a mixed Bessel function. Z. angew. Math. Phys. 39, 157–165 (1988). https://doi.org/10.1007/BF00945762

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  • DOI: https://doi.org/10.1007/BF00945762

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