A novel solution of a lateral connection problem

J. A.M. McHugh

doi:10.1016/0022-0396(73)90023-5

A novel solution of a lateral connection problem

J. A.M. McHugh

Research output: Contribution to journal › Article › peer-review

Abstract

Weber's parabolic cylinder equation, ( d²y dz²) + [v + 1 2 - ( z² 4)] y = 0, (*) has as solutions the parabolic cylinder functions, D_v(z) ~ z^v 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 D_v(z) are not required.

Original language	English (US)
Pages (from-to)	374-383
Number of pages	10
Journal	Journal of Differential Equations
Volume	13
Issue number	2
DOIs	https://doi.org/10.1016/0022-0396(73)90023-5
State	Published - Mar 1973
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/0022-0396(73)90023-5

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title = "A novel solution of a lateral connection problem",

abstract = "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.",

author = "McHugh, {J. A.M.}",

year = "1973",

month = mar,

doi = "10.1016/0022-0396(73)90023-5",

language = "English (US)",

volume = "13",

pages = "374--383",

journal = "Journal of Differential Equations",

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publisher = "Academic Press Inc.",

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T1 - A novel solution of a lateral connection problem

AU - McHugh, J. A.M.

PY - 1973/3

Y1 - 1973/3

N2 - 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.

AB - 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.

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DO - 10.1016/0022-0396(73)90023-5

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SP - 374

EP - 383

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

A novel solution of a lateral connection problem

Abstract

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