r-Dependence in Two-Point Orientation Coherence Functions

Functions are derived, which are orthonormal on the range r=0, 1, with weight function corresponding to the distribution of r in a typical experimental procedure for measurement of the two-point orientation–coherence (or orientation–correlation) function. These are obtained by making an appropriate change of variable in spherical Bessel functions, orthonormal on the range r=0, 1, with unit weight function. The effects of weight function and change of variable on the functions are considered.

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Singular Behavior of the Spectral-Weight Function of the Spin-Pair Correlation Function

Physical Review B ◽

10.1103/physrevb.8.414 ◽

1973 ◽

Vol 8 (1) ◽

pp. 414-417 ◽

Cited By ~ 6

Author(s):

Tohru Morita ◽

Tsuyoshi Horiguchi

Keyword(s):

Correlation Function ◽

Weight Function ◽

Pair Correlation Function ◽

Pair Correlation ◽

Spectral Weight ◽

Singular Behavior ◽

Spin Pair ◽

Spectral Weight Function

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Global asymptotics of the Szegő–Askey polynomials

Analysis and Applications ◽

10.1142/s0219530514500547 ◽

2014 ◽

Vol 12 (06) ◽

pp. 727-746 ◽

Cited By ~ 1

Author(s):

Y. Lin ◽

R. Wong

Keyword(s):

Asymptotic Behavior ◽

Asymptotic Expansion ◽

Weight Function ◽

Unit Circle ◽

Bessel Functions ◽

Asymptotic Formulas ◽

Elementary Functions ◽

Integral Methods ◽

Uniform Asymptotic Expansion ◽

Global Asymptotics

The Szegő–Askey polynomials are orthogonal polynomials on the unit circle. In this paper, we study their asymptotic behavior by knowing only their weight function. Using the Riemann–Hilbert method, we obtain global asymptotic formulas in terms of Bessel functions and elementary functions for z in two overlapping regions, which together cover the whole complex plane. Our results agree with those obtained earlier by Temme [Uniform asymptotic expansion for a class of polynomials biorthogonal on the unit circle, Constr. Approx. 2 (1986) 369–376]. Temme's approach started from an explicit expression of the Szegő–Askey polynomials in terms of an2F1-function, and followed by integral methods.

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Determination of the correlation function directly from slit-smeared small-angle X-ray scattering curves

Journal of Applied Crystallography ◽

10.1107/s0021889882011686 ◽

1982 ◽

Vol 15 (2) ◽

pp. 143-147 ◽

Cited By ~ 8

Author(s):

T. Gerber ◽

G. Walter ◽

R. Kranold

Keyword(s):

Correlation Function ◽

Small Angle ◽

Bessel Functions ◽

Simple Technique ◽

Zero Order ◽

Primary Beam ◽

X Ray ◽

X Ray Scattering ◽

Ray Scattering

A simple technique has been developed for calculating the correlation function directly from small-angle X-ray scattering curves obtained with an `infinitely long' primary beam profile. The method is based on expanding the correlation function in a series of zero-order Bessel functions of the first kind, where the coefficients of the series are proportional to the intensities of the measured curve. The correlation function thus is represented by an analytical expression and can be calculated easily.

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A note on Bessel function dual integral equation with weight function

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171288000651 ◽

1988 ◽

Vol 11 (3) ◽

pp. 543-549 ◽

Cited By ~ 3

Author(s):

B. N. Mandal

Keyword(s):

Integral Equation ◽

Weight Function ◽

Bessel Function ◽

Integral Equations ◽

Fredholm Integral Equation ◽

Bessel Functions ◽

Dual Integral Equation ◽

Dual Integral Equations ◽

Arbitrary Weight

An elementary procedure based on Sonine's integrals has been used to reduce dual integral equations with Bessel functions of different orders as kernels and an arbitrary weight function to a Fredholm integral equation of the second kind. The result obtained here encompasses many results concerning dual integral equations with Bessel functions as kernels known in the literature.

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The combined Herstmonceux Cambridge Program of optical positions of radio sources

International Astronomical Union Colloquium ◽

10.1017/s025292110007408x ◽

1978 ◽

Vol 48 ◽

pp. 155-166 ◽

Cited By ~ 1

Author(s):

A. N. Argue ◽

E. D. Clements ◽

G. M. Harvey ◽

C. A. Murray

Keyword(s):

Standard Error ◽

Unit Weight ◽

Radio Sources

SummaryAGK3-based optical positions are presented for 38 counterparts of radio sources selected from the catalogue of Elsmore & Ryle. The measurements were made from plates taken with the 13-inch Astrograph, the 26-inch refractor and the 2.5 m (INT) reflector at Herstmonceux, and the 17-inch Schmidt at Cambridge. The standard error for a mean position of unit weight is 0”.11, and the weights range from 3.0 for the brightest sources to 0.5 for the faintest. Comparison with the radio positions shows no significant differences. The effects of applying the Brorfelde corrections to AGK3 are discussed.

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