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From: dpb@philabs.UUCP (Paul Benjamin)
Newsgroups: net.math
Subject: Re: Re: Self-generating power series?
Message-ID: <225@philabs.UUCP>
Date: Fri, 1-Feb-85 14:36:44 EST
Article-I.D.: philabs.225
Posted: Fri Feb  1 14:36:44 1985
Date-Received: Wed, 6-Feb-85 01:54:38 EST
References: <1155@ihuxi.UUCP> <1263@ut-ngp.UUCP>
Organization: Philips Labs, Briarcliff Manor, NY
Lines: 47

> > Can anyone find a (nontrivial) power series that, evaluated over the
> > nonnegative integers, gives its own coefficients? That is,
> > 
> >                    oo        n
> >                   ---  A  * x
> >                   \     n
> >         P(x)  =   /    -------    =  A    for  n >= 0
> >                   ---    n!           n
> >                   k=0
> > 
> > 				Chris Scussel
> > 				AT&T Bell Labs
> > 				ihnp4!ihuxi!trough
> 
> Surely you mean P(n)=, as in:
>                    oo        n
>                   ---  A  * x
>                   \     n
>         P(n)  =   /    -------    =  A    for  n >= 0
>                   ---    n!           n
>                   k=0
> 
> -- 
> 
>                                            John L. Templer
>                                      University of Texas at Austin
> 
>     {allegra,gatech,seismo!ut-sally,vortex}!ut-ngp!lindley
> 
>                  "and they called it, yuppy love."

Even more surely you mean:

		    oo         k
                   ---   A  * n
         	   \      k
        P(n)  =    /     -------  =  A   for n >= 0
		   ---     k!         n
		   k=0

                      0
                A  * 0  
                 0                          0
   Since P(0) =  ------- + (zeros) = 0 (if 0  is defined as 0), 
		  0!

   we can change the lower limit of summation to 1.