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airy.omcd
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<OMOBJ xmlns:om="http://www.openmath.org/OpenMath"
xmlns="http://www.openmath.org/OpenMath">
<OMA>
<OMS cd="meta" name="CD"/>
<OMA>
<OMS cd="meta" name="CDComment"/>
<OMSTR>This document is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. The copyright holder grants you permission to redistribute this document freely as a verbatim copy. Furthermore, the copyright holder permits you to develop any derived work from this document provided that the following conditions are met. a) The derived work acknowledges the fact that it is derived from this document, and maintains a prominent reference in the work to the original source. b) The fact that the derived work is not the original OpenMath document is stated prominently in the derived work. Moreover if both this document and the derived work are Content Dictionaries then the derived work must include a different CDName element, chosen so that it cannot be confused with any works adopted by the OpenMath Society. In particular, if there is a Content Dictionary Group whose name is, for example, `math' containing Content Dictionaries named `math1', `math2' etc., then you should not name a derived Content Dictionary `mathN' where N is an integer. However you are free to name it `private_mathN' or some such. This is because the names `mathN' may be used by the OpenMath Society for future extensions. c) The derived work is distributed under terms that allow the compilation of derived works, but keep paragraphs a) and b) intact. The simplest way to do this is to distribute the derived work under the OpenMath license, but this is not a requirement. If you have questions about this license please contact the OpenMath society at http://www.openmath.org.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDName"/>
<OMSTR>airy</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDURL"/>
<OMSTR>http://www.openmath.org/CDs/airy.ocd</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDReviewDate"/>
<OMSTR>2017-12-31</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDDate"/>
<OMSTR>2002-01-19</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDVersion"/>
<OMSTR>1</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDRevision"/>
<OMSTR>2</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDComment"/>
<OMSTR>Author: James Davenport</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDStatus"/>
<OMSTR>experimental</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>This content dictionary contains symbols to describe the Airy functions and associated functions.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Ai</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol Ai defines the unary Airy Ai function; as in Abramovitz & Stegun equation 10.4.1. This is a solution to the equation: $$w^{\prime\prime}-x*w=0$$ It is linearly independent to the Airy Bi function represented by the Bi symbol in this Content Dictionary and is specifically given by: $$Ai(x)=Ai(0)~f(z)-(-Ai^\prime (0))~g(z)$$ where: $$f(z)=\sum_{k=0}^\infty 3^k{\left (\frac{1}{3}\right )}_k \frac{z^{3k}}{(3k)!}$$ and: $$g(z)=\sum_{k=0}^\infty 3^k{\left (\frac{2}{3}\right )}_k \frac{z^{3k+1}}{(3k+1)!}$$</OMSTR>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Bi</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol Bi defines the unary Airy Bi function. This is defined in Abramivitz and Stegun 10.4.1 and is a solution to the equation: $$w^{\prime\prime}-x*w=0$$ It is linearly independant to the Airy Ai function represented by the Ai symbol in this Content Dictionary and is specifically given by: $$Bi(x)=\sqrt{3}(Bi(0)~f(z)+(-Bi^\prime (0))~g(z))$$ where: $$f(z)=\sum_{k=0}^\infty 3^k{\left (\frac{1}{3}\right )}_k \frac{z^{3k}}{(3k)!}$$ and: $$g(z)=\sum_{k=0}^\infty 3^k{\left (\frac{2}{3}\right )}_k \frac{z^{3k+1}}{(3k+1)!}$$</OMSTR>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Ai2</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol Ai2 takes two arguments, it represents derivatives of the Airy Ai function. The symbol Ai2(n,z) represents the n'th derivative of Ai(z).</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<OMA>
<OMS name="eq" cd="relation1"/>
<OMA>
<OMS name="Ai" cd="airy"/>
<OMV name="z"/>
</OMA>
<OMA>
<OMS name="Ai2" cd="airy"/>
<OMS name="zero" cd="alg1"/>
<OMV name="z"/>
</OMA>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<OMA>
<OMS name="eq" cd="relation1"/>
<OMA>
<OMA>
<OMS name="diff" cd="calculus1"/>
<OMBIND>
<OMS name="lambda" cd="fns1"/>
<OMBVAR>
<OMV name="z"/>
</OMBVAR>
<OMA>
<OMS name="Ai2" cd="airy"/>
<OMV name="n"/>
<OMV name="z"/>
</OMA>
</OMBIND>
</OMA>
<OMV name="z"/>
</OMA>
<OMA>
<OMS name="Ai2" cd="airy"/>
<OMA>
<OMS name="plus" cd="arith1"/>
<OMV name="n"/>
<OMS name="one" cd="alg1"/>
</OMA>
<OMV name="z"/>
</OMA>
</OMA>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Bi2</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>The symbol Bi2 takes two arguments, it represents derivatives of the Airy Bi function. The symbol Bi2(n,z) represents the n'th derivative of Bi(z).</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<OMA>
<OMS name="eq" cd="relation1"/>
<OMA>
<OMS name="Bi" cd="airy"/>
<OMV name="z"/>
</OMA>
<OMA>
<OMS name="Bi2" cd="airy"/>
<OMS name="zero" cd="alg1"/>
<OMV name="z"/>
</OMA>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<OMA>
<OMS name="eq" cd="relation1"/>
<OMA>
<OMA>
<OMS name="diff" cd="calculus1"/>
<OMBIND>
<OMS name="lambda" cd="fns1"/>
<OMBVAR>
<OMV name="z"/>
</OMBVAR>
<OMA>
<OMS name="Bi2" cd="airy"/>
<OMV name="n"/>
<OMV name="z"/>
</OMA>
</OMBIND>
</OMA>
<OMV name="z"/>
</OMA>
<OMA>
<OMS name="Bi2" cd="airy"/>
<OMA>
<OMS name="plus" cd="arith1"/>
<OMV name="n"/>
<OMS name="one" cd="alg1"/>
</OMA>
<OMV name="z"/>
</OMA>
</OMA>
</OMA>
</OMA>
</OMA>
</OMOBJ>