A complex definite integral used in the semi-analytical solution of the mass transport equation in an unbounded two- or three-dimensional domain
The author calculates the integral \[ \int^ \infty_ 0 e^{-(t^ 2+{z^ 2\over t^ 2})}dt={\sqrt\pi\over 2}e^{-2z},\quad|\arg z|\leq{\pi\over 4}. \] For positive \(z\) this equality is reported in mathematical tables. For complex \(z\) this equality follows from the theorem of uniqueness for analytic functions. The author gives another proof.
scientific article; zbMATH DE number 62802