The integral ϕ(t, u) = integral e^(π i t x^2 + 2π i u x)/(e^(2π i x) - 1) d x which is related to the Jacobi theta functions, mock theta functions, Riemann zeta function, and Siegel theta function.

Jacobi theta functions | mock theta function | Riemann zeta function | Siegel theta function

Louis Joel Mordell