Bessel’s differential equation

Bessel s Differential Equation. We showed previously 2fi above) that, if n is an integer, J (ie) is a solution of Bessel s equation (2G. )). We shall now examine the solutions of that equation when the parameter n is not necessarily an integer. To emphasise that this parameter is, in general, non-integral, wc shall replace it by the symbol v, so that wc now consider the solutions of the second order linear differential equation... 

The series solution of Bessel s differential equation will provide facts about the Bessel function s behavior near the origin. The series solution is also used to generate the standard function, and tabulated values of Bessel functions. The resulting series solution is... 

The general solution of Bessel s differential equation for noninteger v is given by... 

In Section 8.7, a series solution of Bessel s differential equation was derived, leading to the definition of Bessel functions of the first kind ... 

Another example of a prototype equation that should be familiar to most chemical engineers is Bessel s differential equation of order n... 

In order to solve Bessel s differential equation by comparison one needs a standard form of the equation to compare to. For example, the form... 

Equation 5.62 is a transformed Bessel s differential equation, which has a solution for arbitrary values of the form factor, s, that can be expressed with the Bessel functions. 

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