Generating Functions for Bessel Functions
1959 ◽
Vol 11
◽
pp. 148-155
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Keyword(s):
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).
1991 ◽
Vol 28
(01)
◽
pp. 1-8
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1991 ◽
Vol 33
(2)
◽
pp. 149-163
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1980 ◽
Vol 87
(3)
◽
pp. 515-521
Keyword(s):
1922 ◽
Vol 41
◽
pp. 76-81
1995 ◽
Vol 3
(1)
◽
1994 ◽
Vol 51
(2)
◽
pp. 135-157
◽
1947 ◽
Vol 43
(3)
◽
pp. 348-359
◽