Vibrationdata Bessel Functions Page   by Tom Irvine


Differential Equation



Solution


 Bessel Function of the First Kind

Zero Order

First Order


Order n

n = 0, 1, 2, . . .




Modified Bessel Function of the First Kind

Zero Order

First Order



Higher Order Modified Bessel Function

Bessel Function of the Second Kind (Neumann Functions)

Zero Order


where c = 0.577 215 665


First Order

Modified Bessel Function of the Second Kind

Zero Order

Half-Odd Integers

   
   

Recurrence Relations

First Derivative


 


 Software
Bessel_functions.exe
Bessel_functions.cpp
 Tutorials Referencing Bessel Functions

Newton-Raphson Method Applied to Vibration Problems: Newrap.pdf
Longitudinal Vibration of a Tapered Rod: taper_long.pdf 
Natural Frequencies of Circular Plate Bending Modes: circular.pdf
 Bessel Function Books
__________________________________________________________________________________________________________
Please send comments and questions to Tom Irvine at: tomirvine@aol.com 

Other Math Pages
| math software | Laplace Transforms | Factorial | Euler's Equation | Bessel Function |
| Gamma Function | Partial Fractions | Root of Complex Number
Google
 
Web www.vibrationdata.com