Weber's parabolic cylinder equation, ( d2y dz2) + [v + 1 2 - ( z2 4)] y = 0, (*) has as solutions the parabolic cylinder functions, Dv(z) ~ zv exp(- z2 4), z → + ∞. (**) The expansion (**) is generally not valid for z → - ∞. This situation leads to the so-called "lateral connection problem" for (*). A novel method of solution of this problem based on the Hadamard factorization theorem applied to the "lateral connection coefficient" is given. Unlike previous methods, explicit contour integrals for Dv(z) are not required.
All Science Journal Classification (ASJC) codes
- Applied Mathematics