Author(s): Emerson B. S. Corrêa*, Carlos A Bahia and Michelli S. R. Sarges
We study four expressions involving the integrals of Jacobi’s theta functions. From Poisson’s summation formula, we write the integrals of the functions θi, (i = 1,2,3,4) in terms of modified Bessel functions of the second kind. For the integrals of θ1, θ2 and θ3, we get expressions with real arguments, but for the integral of θ4, we find an expression with imaginary argument. In addition, we apply our results to the description of two kinds of interacting quantum systems: boson gas and fermion gas both under a thermal bath and an external magnetic field.
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