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Solutions of the Differential Equation u ‴+λ 2 zu +(α−1)λ 2 u =0
Author(s) -
Hershenov Joseph
Publication year - 1976
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1976554301
Subject(s) - mathematics , differential equation , integer (computer science) , mathematical analysis , constant (computer programming) , series (stratigraphy) , mathematical physics , first order partial differential equation , paleontology , computer science , biology , programming language
This paper deals with the solutions of the differential equation u ‴+λ 2 zu +(α−1)λ 2 u =0, in which λ is a complex parameter of large absolute value and α is an arbitrary constant, real or complex. After a discussion of the structure of the solutions of the differential equation, an integral representation of the solution is given, from which the series solutions and their asymptotic representations are derived. A third independent solution is needed for the special case when α−1 is a positive integer, and two derivations for this are given. Finally, a comparison is made with the results obtained by R. E. Langer.