scholarly journals The Analysis of Large Order Bessel Functions in Gravitational Wave Signals from Pulsars

2005 ◽  
Author(s):  
F.A. Chishtie ◽  
S.R. Valluri ◽  
K.M. Rao ◽  
D. Sikorski ◽  
T. Williams
Keyword(s):  
Gravitational Wave ◽  
Bessel Functions ◽  
Large Order

scholarly journals AN INVESTIGATION OF UNIFORM EXPANSIONS OF LARGE ORDER BESSEL FUNCTIONS IN GRAVITATIONAL WAVE SIGNALS

2008 ◽  
Vol 17 (08) ◽  
pp. 1197-1212 ◽  
Author(s):  
F. A. CHISHTIE ◽  
K. M. RAO ◽  
I. S. KOTSIREAS ◽  
S. R. VALLURI
Keyword(s):  
Gravitational Wave ◽  
Entire Range ◽  
Bessel Functions ◽  
Tomographic Reconstruction ◽  
Matched Filtering ◽  
Global Parameter ◽  
Large Order ◽  
The Fourier Transform ◽  
Uniform Expansions ◽  
Uniform Expansion

In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of applications, particularly the Fourier transform (FT) of the gravitational wave (GW) signal from a pulsar, global parameter space correlations of a coherent matched filtering search for continuous GWs from isolated neutron stars and tomographic reconstruction of GW LISA sources. The uniform expansion we consider here is found to be valid in the entire range of the argument.

scholarly journals The resurgence properties of the large-order asymptotics of the Hankel and Bessel functions

2014 ◽  
Vol 12 (04) ◽  
pp. 403-462 ◽  
Author(s):  
Gergő Nemes
Keyword(s):  
Error Bounds ◽  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Smooth Transition ◽  
Large Order ◽  
Computable Error Bounds

The aim of this paper is to derive new representations for the Hankel and Bessel functions, exploiting the reformulation of the method of steepest descents by Berry and Howls [Hyperasymptotics for integrals with saddles, Proc. R. Soc. Lond. A 434 (1991) 657–675]. Using these representations, we obtain a number of properties of the large-order asymptotic expansions of the Hankel and Bessel functions due to Debye, including explicit and numerically computable error bounds, asymptotics for the late coefficients, exponentially improved asymptotic expansions, and the smooth transition of the Stokes discontinuities.

The asymptotic expansion of bessel functions of large order

1954 ◽  
Vol 247 (930) ◽  
pp. 328-368 ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Bessel Functions ◽  
Airy Functions ◽  
Elementary Functions ◽  
Large Order ◽  
Hankel Functions ◽  
Rapid Calculation ◽  
Zeros Of Functions ◽  
Significant Figures ◽  
Complex Zeros

New expansions are obtained for the functions Iv{yz), ) and their derivatives in terms of elementary functions, and for the functions J v(vz), Yv{vz), H fvz) and their derivatives in terms of Airy functions, which are uniformly valid with respect to z when | | is large. New series for the zeros and associated values are derived by reversion and used to determine the distribution of the zeros of functions of large order in the z-plane. Particular attention is paid to the complex zeros of 7„(z) and the Hankel functions when the order n is an integer or half an odd integer, and for this purpose some new asymptotic expansions of the Airy functions are derived. Tables are given of complex zeros of Airy functions and other quantities which facilitate the rapid calculation of the smaller complex zeros of 7„(z), 7'(z), and the Hankel functions and their derivatives, when 2 n is an integer, to an accuracy of three or four significant figures.

XIX.—On the Determination of the General Term in Green-type Expansions

1967 ◽  
Vol 67 (4) ◽  
pp. 243-255
Author(s):  
S. Jorna
Keyword(s):  
Series Expansion ◽  
Bessel Functions ◽  
Formal Method ◽  
General Term ◽  
Modified Bessel Functions ◽  
Large Order

SynopsisA formal method is developed for deriving a series expansion of the general term in Green-type expansions. The technique is exemplified by detailed calculations for modified Bessel functions of large order.

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