# The imaginary zeros of a mixed Bessel function

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

## Abstract

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.

## Keywords

Lower Bound Mathematical Method Bessel Function Monotonicity Property Imaginary Zero
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Zusammenfassung

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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