Advanced Engineering Mathematics, 7th Edition

5.3 Special Functions

INTRODUCTION

The two differential equations

(1)

(2)

often arise in the advanced studies of applied mathematics, physics, and engineering. Equation (1) is called Bessel’s equation of order ν and is named after the noted German astronomer and mathematician Friedrich Wilhelm Bessel (1784–1846), who was the first person to determine the accurate distance from the Sun to another star. Bessel first encountered a special form of equation (1) in his study of elliptical planetary motion and eventually carried out a systematic study ...