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Mathematical Notes

, Volume 98, Issue 5–6, pp 714–724 | Cite as

On a remarkable sequence of Bessel matrices

  • V. M. Bukhshtaber
  • S. I. Tertychnyi
Article

Abstract

A sequence of matrices whose elements are modified Bessel functions of the first kind is considered. Such a sequence arises when studying certain ordinary linear homogeneous second-order differential equations belonging to the family of double confluent Heun equations. The conjecture that these matrices are nonsingular is discussed together with its application to the problem of the existence of solutions analytic at the singular point of the equation referred to above.

Keywords

modified Bessel function of the first kind double confluent Heun equation Bessel matrix Josephson junction Laurent series Hessenberg matrix 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  2. 2.All-Russia Scientific Research Institute of Physical and Radio Engineering MeasurementsMendeleevoRussia

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