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Theta functions identites

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#complex-analysis #riemann-surfaces #theta-functions
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how to prove these formulas about infinite product?

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#calculus #theta-functions #q-series #modular-function
144
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Evaluation of $\sum_{n=1}^{\infty}q^{n^{2}}$?

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#sequences-and-series #theta-functions
88
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evaluation of $\sum_{n=-\infty}^{\infty}e^{-2\pi^{2}z^{2}n^{2}}$ for large z

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#sequences-and-series #theta-functions #euler-maclaurin
126
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Resources for learning about theta functions

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#online-resources #theta-functions
43
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$\sum_i^{\infty}e^{(-(2i+1)^2a)}(2i+1)^2$ where a is is a positive real number

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#sequences-and-series #special-functions #theta-functions
55
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A closed form for these non-elementary, generalized relatives of the geometric series

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#sequences-and-series #analysis #power-series #closed-form #theta-functions
67
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The estimate for $\sum_{0}^{\infty} e^{-kn^2}-e^{-k(n+1/2)^2}$

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#complex-analysis #limits #analysis #theta-functions
191
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How is the integral form of Ramanujan theta function derived?

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#integration #sequences-and-series #integral-transforms #theta-functions
658
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A problem posed by Ramanujan involving $\sum e^{-5\pi n^2}$

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#sequences-and-series #theta-functions
276
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Determine values of $\theta$ for which $\arg(z-4+2i)=\theta$ and $|z+6+6i|=4$ have no common solutions

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#complex-numbers #locus #theta-functions
369
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What are specific proofs of Jacobi Triple Product Identity?

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#combinatorics #theta-functions #q-series
747
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Summation of $\sum_{n=0}^{\infty}a^nq^{n^2}$

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#summation #fourier-transform #theta-functions #pochhammer-symbol
175
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How to prove that this is a zero of the theta function?

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#theta-functions
2.2k
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Curious integrals for Jacobi Theta Functions $\int_0^1 \vartheta_n(0,q)dq$

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#integration #definite-integrals #hyperbolic-functions #elliptic-functions #theta-functions

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