Asymptotic expansion of ∫0π⁄2 Jv2 (λ cos θ) dθ

R. Wong

doi:10.1090/S0025-5718-1988-0917830-2

Asymptotic expansion of ∫₀^π^⁄2J_v²(λ cos θ) dθ

R. Wong

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

13 Citations (Scopus)

Abstract

An asymptotic expansion is obtained, as λ →+∞, for the integral
I(λ) = ∫₀^π^⁄2J_v²(λ cos θ) dθ
where J_v(t) is the Bessel function of the first kind and ν > - ½. This integral arises in studies of crystallography and diffraction theory. We show in particular that I/(λ) ∼ In λ /λπ. © 1988 American Mathematical Society.

Original language	English
Pages (from-to)	229-234
Journal	Mathematics of Computation
Volume	50
Issue number	181
DOIs	https://doi.org/10.1090/S0025-5718-1988-0917830-2
Publication status	Published - Jan 1988
Externally published	Yes

Research Keywords

Asymptotic expansion
Bessel functions
Mellin transforms

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abstract = "An asymptotic expansion is obtained, as λ →+∞, for the integral I(λ) = ∫0π⁄2 Jv2 (λ cos θ) dθwhere Jv(t) is the Bessel function of the first kind and ν > - ½. This integral arises in studies of crystallography and diffraction theory. We show in particular that I/(λ) ∼ In λ /λπ. {\textcopyright} 1988 American Mathematical Society.",

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T1 - Asymptotic expansion of ∫0π⁄2 Jv2 (λ cos θ) dθ

AU - Wong, R.

PY - 1988/1

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N2 - An asymptotic expansion is obtained, as λ →+∞, for the integral I(λ) = ∫0π⁄2 Jv2 (λ cos θ) dθwhere Jv(t) is the Bessel function of the first kind and ν > - ½. This integral arises in studies of crystallography and diffraction theory. We show in particular that I/(λ) ∼ In λ /λπ. © 1988 American Mathematical Society.

AB - An asymptotic expansion is obtained, as λ →+∞, for the integral I(λ) = ∫0π⁄2 Jv2 (λ cos θ) dθwhere Jv(t) is the Bessel function of the first kind and ν > - ½. This integral arises in studies of crystallography and diffraction theory. We show in particular that I/(λ) ∼ In λ /λπ. © 1988 American Mathematical Society.

KW - Asymptotic expansion

KW - Bessel functions

KW - Mellin transforms

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U2 - 10.1090/S0025-5718-1988-0917830-2

DO - 10.1090/S0025-5718-1988-0917830-2

M3 - RGC 21 - Publication in refereed journal

SN - 0025-5718

VL - 50

SP - 229

EP - 234

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 181

ER -