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Self-Reciprocal Functions Involving Laguerre Polynomials
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The object of this note is to prove that the function
x-1/2e-1/2x2L1/2r-1/2n(1/2x2)
is self-reciprocal for Jr transforms, where n is a positive integer.
Adopting a similar procedure, I also obtain the result that the function
xr+2n+1/2e-1/2x2Ln+rn(1/2x2),
where n is a positive integer, is self-reciprocal for Jr transforms, a theorem proved otherwise by Howell.
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