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1956•Canadian Journal of MathematicsOpen access

Asymptotic Solution Of Differential Equations In a Domain Containing a Regular Singular Point

Nicholas D. Kazarinoff, ROBERT W. MCKELVEY

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Abstract

1. Introduction. In this paper we study the asymptotic behavior in λ of the solutions about the origin in the z-plane of the differential equation . Both the variable z and the parameter λ are complex. The coefficient P(z, λ) is assumed to be analytic and single-valued in λ at infinity and in z throughout a bounded, closed, simply connected domain D containing z = 0.

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1. Introduction. In this paper we study the asymptotic behavior in λ of the solutions about the origin in the z-plane of the differential equation . Both the variable z and the parameter λ are complex. The coefficient P(z, λ) is assumed to be analytic and single-valued in λ at infinity and in z throughout a bounded, closed, simply connected domain D containing z = 0.

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Available abstract

1. Introduction. In this paper we study the asymptotic behavior in λ of the solutions about the origin in the z-plane of the differential equation . Both the variable z and the parameter λ are complex. The coefficient P(z, λ) is assumed to be analytic and single-valued in λ at infinity and in z throughout a bounded, closed, simply connected domain D containing z = 0.

Key concepts: Mathematics, Bounded function, Domain (mathematical analysis), Infinity, Mathematical analysis, Singular point of a curve, Plane (geometry), Regular singular point

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