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Formula:KLS:09.15:14 - Revision history
2024-03-28T13:40:24Z
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2019-12-22T06:36:19Z
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https://drmf-beta.wmflabs.org/index.php?title=Formula:KLS:09.15:14&diff=1966&oldid=prev
imported>SeedBot: DRMF
2017-03-05T22:34:28Z
<p>DRMF</p>
<p><b>New page</b></p><div>{{DISPLAYTITLE:Formula:KLS:09.15:14}}<br />
<div id="drmf_head"><br />
<div id="alignleft"> << [[Formula:KLS:09.15:13|Formula:KLS:09.15:13]] </div><br />
<div id="aligncenter"> [[Hermite#KLS:09.15:14|formula in Hermite]] </div><br />
<div id="alignright"> [[Formula:KLS:09.15:15|Formula:KLS:09.15:15]] >> </div><br />
</div><br />
<br />
<br /><div align="center"><math>{\displaystyle <br />
\expe^{-t^2}\cosh@{2xt}=\sum_{n=0}^{\infty}<br />
\frac{\Hermite{2n}@{x}}{(2n)!}t^{2n}<br />
}</math></div><br />
<br />
== Proof ==<br />
<br />
We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.<br />
<br />
== Symbols List ==<br />
<br />
<span class="plainlinks">[http://dlmf.nist.gov/4.2.E11 <math>{\displaystyle \mathrm{e}}</math>]</span> : the base of the natural logarithm : [http://dlmf.nist.gov/4.2.E11 http://dlmf.nist.gov/4.2.E11]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/4.28#E2 <math>{\displaystyle \mathrm{cosh}}</math>]</span> : hyperbolic cosine function : [http://dlmf.nist.gov/4.28#E2 http://dlmf.nist.gov/4.28#E2]<br /><br />
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:sum <math>{\displaystyle \Sigma}</math>]</span> : sum : [http://drmf.wmflabs.org/wiki/Definition:sum http://drmf.wmflabs.org/wiki/Definition:sum]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/18.3#T1.t1.r28 <math>{\displaystyle H_{n}}</math>]</span> : Hermite polynomial <math>{\displaystyle H_n}</math> : [http://dlmf.nist.gov/18.3#T1.t1.r28 http://dlmf.nist.gov/18.3#T1.t1.r28]<br />
<br /><br />
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== Bibliography==<br />
<br />
<span class="plainlinks">[http://homepage.tudelft.nl/11r49/askey/contents.html Equation in Section 9.15]</span> of [[Bibliography#KLS|'''KLS''']].<br />
<br />
== URL links ==<br />
<br />
We ask users to provide relevant URL links in this space.<br />
<br />
<br /><div id="drmf_foot"><br />
<div id="alignleft"> << [[Formula:KLS:09.15:13|Formula:KLS:09.15:13]] </div><br />
<div id="aligncenter"> [[Hermite#KLS:09.15:14|formula in Hermite]] </div><br />
<div id="alignright"> [[Formula:KLS:09.15:15|Formula:KLS:09.15:15]] >> </div><br />
</div></div>
imported>SeedBot