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How to prove the $q$-series identity?

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#number-theory #q-series
145
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improper integrals in q-calculus

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#real-analysis #special-functions #improper-integrals #q-series #quantum-calculus
155
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double integrals on quantum calculus

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#reference-request #book-recommendation #q-series #quantum-calculus
375
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Show that $\prod\limits_{n=1}^\infty \frac{(1-q^{6n})(1-q^n)^2}{(1-q^{3n})(1-q^{2n})}=\sum\limits_{n=-\infty}^\infty q^{2n^2+n}-3q^{9(2n^2+n)+1}$.

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#modular-forms #theta-functions #q-series
87
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Reference request: $q$-gamma, $q$-polygamma, $q$-Pochhammer.

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#reference-request #gamma-function #polygamma #q-series #pochhammer-symbol
416
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how to prove these formulas about infinite product?

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#calculus #theta-functions #q-series #modular-function
154
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Asymptotics of the quantum dilogarithm

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#complex-analysis #asymptotics #q-series
257
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An equivalent of Jacobi's two square theorem

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#number-theory #sums-of-squares #q-series
369
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What are specific proofs of Jacobi Triple Product Identity?

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#combinatorics #theta-functions #q-series
251
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what is the expansion for $\log \sum q^{n^2}$?

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#power-series #special-functions #theta-functions #q-series
114
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What are the $q$ Power Series?

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#modular-forms #q-series
205
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Proving $\frac 1{R(q)}-1-R(q)$ (Ramanujan's formula)

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#sequences-and-series #continued-fractions #modular-forms #q-series
540
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Relation between Ramanujan Theta Function and Jacobi Theta Function

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#combinatorics #complex-analysis #number-theory #modular-forms #q-series
219
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Parity of Ramanujan's Tau Function

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#combinatorics #elementary-number-theory #infinite-product #parity #q-series
102
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Identity involving q-Pochhammer symbols -- "Normalization"

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#combinatorics #induction #binomial-coefficients #q-series #pochhammer-symbol

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