series sum

nipunmalhotra

what is the sum of the following series? I know it's convergent (using ratio test) but I'm not able to work it out :(
S=t^(-1) + t^(-4)+t^(-9)............t^(k^2)......to ∞
where t>1
Thanks

Norwegian

S = [θ₃(1/t)-1]/2, where θ₃ is a Jacobi theta function. I strongly suspect S is transcendental for integer t, but couldnt easily find a good reference, nor a convincing argument.

ZARman

Hey everyone
Im a maths tutor and this question was given to one of my students. i may be thinking about it to cryptically so i thought id post it

5,9,13 ,27,,,217

i have posted it to various other pupils but no one has gotten it yet.

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nipunmalhotra	series sum Tweet what is the sum of the following series? I know it's convergent (using ratio test) but I'm not able to work it out :( S=t^(-1) + t^(-4)+t^(-9)............t^(k^2)......to ∞ where t>1 Thanks

Norwegian	S = [θ₃(1/t)-1]/2, where θ₃ is a Jacobi theta function. I strongly suspect S is transcendental for integer t, but couldnt easily find a good reference, nor a convincing argument.

ZARman	Hey everyone Im a maths tutor and this question was given to one of my students. i may be thinking about it to cryptically so i thought id post it 5,9,13 ,27,,,217 i have posted it to various other pupils but no one has gotten it yet.