[seqfan] Re: Fw: Closed form?
Prof. Dr. Alois Heinz
heinz at hs-heilbronn.de
Fri May 1 19:13:39 CEST 2009
Maximilian Hasler schrieb:
>>I have looked at a larger range now, and a(n)/f(n) is drifting slowly
>>upwards or downwards, always with prefix .9233
>>
>>
>Don't you think that this "drifting up and down" corresponds to the
>periodic variation in the Phi function as per Philippe's comment
>[quoted below], and thus won't disappear ?
>
>
yes, of course, that is is. Since Phi is not already encoded into f.
>>Digits:=160:
>>
>>
>
>^^^ I don't understand this, if we are only interested in the first 10
>digits of the ratio a(n)/f(n).
>Would Maple compute the first 10 digits of f(x) incorrectly without this ?
>
>
That's right. At least my (older) version of Maple would not evaluate
f(x) as a float
if the value of Digits is set too low. An example:
> restart;
> Digits:=100:
> f:= proc(x) option remember; evalf (sum (x^k/k!/2^binomial(k,2),
k=0..infinity)) end:
> f (2^90);
.225048982437778079564155816798811340218952734375587207935654152\
1101
3571947332124963929457635315460870670 10
> restart;
> Digits:=50:
> f:= proc(x) option remember; evalf (sum (x^k/k!/2^binomial(k,2),
k=0..infinity)) end:
> f (2^90);
infinity
----- k
\ 1237940039285380274899124224
) -----------------------------
/ binomial(k, 2)
----- k! 2
k = 0
Alois
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