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dtiwari
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If
and
then
By Sterling,
is asymptotically
. Finally, by summation, the expression from the statement converges to some positive constant. I don't think that constant can be "calculated".
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Euclid
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? n = 10^10
%41 = 10000000000
? sqrt(n) * intnum(x=0, Pi/4, cos(x)^(2*n))
%42 = 0.886226925441085374620933874004813917848174[...]
? sqrt(Pi)/2
%43 = 0.886226925452758013649083741670572591398774[...]
(Results were manually truncated, used precision was 100 digits.)
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df (gauss)
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Gauss is right... the key idea can be also used to reduce the limit to
(not that the upper limit of the integral is now
).
And that integral is easily shown to be equal to
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Euclid
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Thanks Admin,s got it.
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dtiwari
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