scholarly journals Integral formulas associated with products of Bessel functions: a new partial differential equation approach

1994 ◽  
Vol 51 (2) ◽  
pp. 135-157 ◽  
Author(s):  
E. Görlich ◽  
C. Markett ◽  
O. Stüpp
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Bessel Functions ◽  
Equation Approach ◽  
Partial Differential ◽  
Integral Formulas

scholarly journals Generating Functions for Bessel Functions

1959 ◽  
Vol 11 ◽  
pp. 148-155 ◽  
Author(s):  
Louis Weisner
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Generating Function ◽  
Lie Group ◽  
Generating Functions ◽  
Bessel Functions ◽  
Partial Differential ◽  
Systematic Determination ◽  
Image Position

On replacing the parameter n in Bessel's differential equation1.1by the operator y(∂/∂y), the partial differential equation Lu = 0 is constructed, where1.2This operator annuls u(x, y) = v(x)yn if, and only if, v(x) satisfies (1.1) and hence is a cylindrical function of order n. Thus every generating function of a set of cylindrical functions is a solution of Lu = 0.It is shown in § 2 that the partial differential equation Lu = 0 is invariant under a three-parameter Lie group. This group is then applied to the systematic determination of generating functions for Bessel functions, following the methods employed in two previous papers (4; 5).

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