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



ksoileau
Posts:
85
From:
Houston, TX
Registered:
3/9/08


Gamma Function  Bessel Function Identity
Posted:
Sep 6, 2012 10:43 AM


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



