Re: Series sin(n^2)/n

On Apr 1, 6:10 pm, amy666 <tommy1...@xxxxxxxxxxx> wrote:
btw tommy1729 used to investigate the more general case

partial sums of (a^n)*sin(n^b)/n^c with a b and c values that prevent convergeance.

he also investigated partial products of type
1 + a^2 + 2a sin(n) which diverges but for 1 > a => 0 they still are bounded above and below.

he gave upper and lower bounds.

perhaps you are intrested.

also of intrest to him where questions like these :

for 1 > a => 0 the partial products of 1 + p(a) + p'(a) f(n) are bounded above and below.

then for a given polynomial p(a) give an equation that descibes all possible smooth f(x) with period pi.

i guess you already know all of that , but just in case you might have been intrested.

( btw he arguments the use of his periodic inverse hypergeo functions for the hardest variants of these kind of problems despite admitting he is stuck on certain parts of his theory relating partial products upperbounds and periodic inverse hypergeometric functions (PIHF), yet he thinks he can fix this with a better understanding of addition formulas for PIHF and a few related numerical integrals ... )

regards

amy

o, i know tommy1729 posted the upper and lwer bounds

ill get you the post

kisses

amy
.

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