A novel solution of a lateral connection problem

J. A.M. McHugh

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)374-383
Number of pages10
JournalJournal of Differential Equations
Issue number2
StatePublished - Mar 1973
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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