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<html><head><meta http-equiv="Content-Style-Type" content="text/html; charset=UTF-8" /> | ||
<style type="text/css" media="all"> @import "m2html.css";</style> | ||
<title>jLab Help Files</title></head><body> | ||
<div><h1>BESSELITILDE is the <a href="jOceans.html">jOceans</a> module of <a href="jLab.html">jLab</a>.</h1></div><div class="fragment"><pre class="comment"> | ||
<a href="besselitilde.html">BESSELITILDE</a> I-type Bessel function after factoring off exponential growth. | ||
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ITILDE=<a href="besselitilde.html">BESSELITILDE</a>(NU,Z) returns the modified Bessel function of the | ||
first kind of order NU at argument Z, after factoring off the | ||
asymptotic behavior of EXP(Z). | ||
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<a href="besselitilde.html">BESSELITILDE</a> is useful for products of modified Bessel functions in | ||
which the exponential behaviors cancel, but that cannot be evaluated | ||
directly because of numerical overflow. | ||
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<a href="besselitilde.html">BESSELITILDE</a>(NU,Z,N) use a summation truncated at N terms. The default | ||
behavior uses N=30 and is highly accurate. | ||
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See 10.40.1 of https://dlmf.nist.gov/10.40. | ||
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This is low-level code used by <a href="windtrans.html">WINDTRANS</a> using an algorithm described | ||
in Lilly and Elipot (2021). | ||
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See also <a href="besselktilde.html">BESSELKTILDE</a>. | ||
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'<a href="besselitilde.html">besselitilde</a> --t' runs a test. | ||
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Usage: I=<a href="besselitilde.html">besselitilde</a>(nu,z); | ||
I=<a href="besselitilde.html">besselitilde</a>(nu,z,nterms); | ||
__________________________________________________________________ | ||
This is part of <a href="jLab.html">JLAB</a> --- type 'help jlab' for more information | ||
(C) 2019--2021 J.M. Lilly --- type 'help <a href="jlab_license.html">jlab_license</a>' for details | ||
</pre></div><h2><a href="jLab.html">contents</a> | <a href="jlab_allhelp.html">allhelp</a> | <a href="jlab_index.html">index</a></h2></body></html> |
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<html><head><meta http-equiv="Content-Style-Type" content="text/html; charset=UTF-8" /> | ||
<style type="text/css" media="all"> @import "m2html.css";</style> | ||
<title>jLab Help Files</title></head><body> | ||
<div><h1>BESSELKTILDE is the <a href="jOceans.html">jOceans</a> module of <a href="jLab.html">jLab</a>.</h1></div><div class="fragment"><pre class="comment"> | ||
<a href="besselktilde.html">BESSELKTILDE</a> K-type Bessel function after factoring off exponential decay. | ||
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KTILDE=<a href="besselktilde.html">BESSELKTILDE</a>(NU,Z) returns the modified Bessel function of the | ||
second kind of order NU at argument Z, after factoring off the | ||
asymptotic behavior of EXP(-Z). | ||
|
||
<a href="besselktilde.html">BESSELKTILDE</a> is useful for products of modified Bessel functions in | ||
which the exponential behaviors cancel, but that cannot be evaluated | ||
directly because of numerical overflow. | ||
|
||
<a href="besselitilde.html">BESSELITILDE</a>(NU,Z,N) use a summation truncated at N terms. The default | ||
behavior uses N=30 and is highly accurate. | ||
|
||
See 10.40.2 of https://dlmf.nist.gov/10.40. | ||
|
||
This is low-level code used by <a href="windtrans.html">WINDTRANS</a> using an algorithm described | ||
in Lilly and Elipot (2021). | ||
|
||
See also <a href="besselitilde.html">BESSELITILDE</a>. | ||
|
||
'<a href="besselktilde.html">besselktilde</a> --t' runs a test. | ||
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||
Usage: K=<a href="besselktilde.html">besselktilde</a>(nu,z); | ||
K=<a href="besselktilde.html">besselktilde</a>(nu,z,nterms); | ||
__________________________________________________________________ | ||
This is part of <a href="jLab.html">JLAB</a> --- type 'help jlab' for more information | ||
(C) 2019--2021 J.M. Lilly --- type 'help <a href="jlab_license.html">jlab_license</a>' for details | ||
</pre></div><h2><a href="jLab.html">contents</a> | <a href="jlab_allhelp.html">allhelp</a> | <a href="jlab_index.html">index</a></h2></body></html> |
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