The imaginary zeros of a mixed Bessel function

  • E. K. Ifantis
  • P. D. Siafarikas
  • C. B. Kouris
Original Papers


In the present work we study the existence and monotonicity properties of the imaginary zeros of the mixed Bessel functionMv(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 andHv(z)=αJv(z)+zJ′v(z), whereJv(z) is the Bessel function of the first kind and of orderv>−1 andJ′v(z), J″v(z) are the first two derivatives ofJv(z). Upper and lower bounds found for the imaginary zeros of the functionsJ′v(z), J″v(z) andHv(z) improve previously known bounds.


Lower Bound Mathematical Method Bessel Function Monotonicity Property Imaginary Zero 
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Dieser Artikel betrifft die Existenz und Monotonie von Eigenschaften imaginärer Nullen der gemischten BesselfunktionMv(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) undHv(z)=αJv(z)+zJ′v(z), woJv(z)die Besselfunktion von erster Art und Ordnungv>−1 andJ′v(z), J″v(z) sind die erste und zweite Ableitung vonJv(z). Untere und obere Schranken, die für die imaginären Nullen der FunktionenJ′v(z), J″v(z) undHv(z) gefunden wurden, verbessern früher bekannte Resultate.


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Copyright information

© Birkhäuser Verlag Basel 1988

Authors and Affiliations

  • E. K. Ifantis
    • 1
  • P. D. Siafarikas
    • 1
  • C. B. Kouris
    • 2
  1. 1.Dept. of MathematicsUniversity of PatrasGreece
  2. 2.National Research Center for Physical Sciences “Demokritos”, Aghia Paraskevi AttikisAthensGreece

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