THE INTEGRAL REPRESENTATION FOR THE PRODUCT OF TWO PARABOLIC CYLINDER FUNCTIONS Dν(x)Dν(−x) AT Re ν < 0 BY MEANS OF THE FUNDAMENTAL SOLUTION OF A LANDAU-TYPE OPERATOR

  • C. Malyshev
  • Published 2008
The fundamental solution (Green’s function) of a first order matrix ordinary differential equation arising in a Landau-type problem is calculated by two methods. The coincidence of the two representations results in the integral formula for the product of two parabolic cylinder functions Dν(x)Dν(−x) at Re ν < 0, x ∈ IR. PDMI Preprint 04/2001 math-ca/0106142