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Unit 1: Bessel s Functions

1.10 Review Questions Notes

Prove that:

2
d J 0 ( ) 1 dJ 0
x
x
x
1. J 2 ( ) 2 x ( )
dx dx
2
d J 0 ( )
x
x
x
2. J 2 ( ) J 0 ( ) 2 2
dx
2
dJ 0 d J 0
x
x
3. J 2 ( ) 3 4 2 ( ) 0
dx dx
d
x
x
x
4. 2 J n ( ) J n 1 ( ) J n 1 ( )
dx
5. Solve the Differential equation
2
d y dy 2 9
x 2 2 x x y 0
dx dx 4
and show that
x
x
y A J 3 ( ) BJ 3 ( )
2 2
1.11 Further Readings
G. N. Watson, A Treatise on the Theory of Bessel Functions
Louis A. Pipes and L.R. Harvill, Applied Mathematics for Engineers and Physicists
K. Yosida, Lectures on Differential and Integral Equations
Jai Dev Anand, P.K. Mittal and Ajay Wadhwa, Mathematical Physics Part II

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