We shall answer a question of Mez\H{o} on the $q$-analogue of the Raabe's integral formula for $0<q<1$ and we shall evaluate an integral involving the first theta function. Moreover, we will reproduce short proofs for some identities of Mez\H{o}.
Orbits of Jacobi forms and Theta relations
Periods of modular forms on $Γ_0(N)$ and products of Jacobi theta functions
A New Proof For The Transformation Laws of Theta Functions
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