Proof of Bessel's Relation: Part I

1 Pages Posted: 19 Sep 2017

Date Written: September 18, 2006


Bessel's equation arises when finding separable solutions to Laplace's equation and the Helmholtz equation in cylindrical or spherical coordinates. Bessel functions are therefore especially important for many problems of wave propagation and static potentials. In solving problems in cylindrical coordinate systems, one obtains Bessel functions of integer order (v = n); in spherical problems, one obtains half-integer orders (v = n ± ½). This paper claims that a Bessel function of higher order can be expressed by Bessel functions of lower orders.

Keywords: Bessel, recurrence, equation, mathematical proof

JEL Classification: C00, C30, C02

Suggested Citation

Nofal, Christopher Paul, Proof of Bessel's Relation: Part I (September 18, 2006). Available at SSRN: or

Christopher Paul Nofal (Contact Author)

Northwestern University School of Law ( email )

375 East Chicago Ave
Chicago, IL 60611
United States


University of Florida College of Engineering ( email )

303 Weil Hall
Gainesville, FL 32611-6595
United States

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