Some new sums of q-trigonometric and related functions through a theta product of Jacobi
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trigonometricfunctionssumsdigammajacobiproductsometheta
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We evaluate some finite and infinite sums involving $q$-trigonometric and $q$-digamma functions. Upon letting $q$ approach $1$, one obtains corresponding sums for the classical trigonometric and the digamma functions. Our key argument is a theta product formula of Jacobi and Gosper's $q$-trigonometric identities.
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