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Topic:
Gamma Function  Bessel Function Identity
Replies:
3
Last Post:
Sep 24, 2012 5:30 AM




Re: Gamma Function  Bessel Function Identity
Posted:
Sep 7, 2012 4:35 PM


On 20120906, ksoileau <kmsoileau@gmail.com> wrote: > I have observed and proved the following identity for all x\ne 0 : > $$ > (I_{k1}(x) +I_{k+1}(x) )I_{k}(x) > (I_{k1}(x)+I_{k+1}(x))I_k(x) > = \frac{4 k}{x \Gamma (1k) \Gamma (1+k)} > $$ > > Is this wellknown or trivially derived? Any comments will be appreciated. > Thanks, > Kerry M. Soileau
I am unaware of it, but the right side can be greatly simplified to 4 sin(k\pi)/(x\pi); it might be known in this form.
 This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558



