HYPERDIRE—HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella function of three variables

详细信息    查看全文

• 作者：Vladimir V. Bytevp>ap>p> ; p>p>bp>p> ; p>p>bvv@jinr.ru" class="auth_mail" title="E-mail the corresponding authorp> ; Bernd A. Kniehlp>ap>p> ; p>p>kniehl@desy.de" class="auth_mail" title="E-mail the corresponding authorp>
• 关键词：Feynman integrals ; Generalized hypergeometric functions ; Differential reduction
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：206
• 期：Complete
• 页码：78-83
• 全文大小：394 K

文摘

We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301059&_mathId=si1.gif&_user=111111111&_pii=S0010465516301059&_rdoc=1&_issn=00104655&md5=5ab347796950cd505c439ec15d0d8212" title="Click to view the MathML source">F_Cpan>pan class="mathContainer hidden">pan class="mathCode">$F_C$pan>pan>pan> of three variables.p>

Program summary

<p id="sp000010">Program title: HYPERDIREp><p id="sp000015">Catalogue identifier: AEPP_v4_0p><p id="sp000020">Program summary URL:pan id="ir000010" class="interref" data-locatorType="url" data-locatorKey="http://cpc.cs.qub.ac.uk/summaries/AEPP_v4_0.html">http://cpc.cs.qub.ac.uk/summaries/AEPP_v4_0.htmlpan>p><p id="sp000025">Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Irelandp><p id="sp000030">Licensing provisions: GNU General Public License, version 3p><p id="sp000035">No. of lines in distributed program, including test data, etc.: 243461p><p id="sp000040">No. of bytes in distributed program, including test data, etc.: 61610782p><p id="sp000045">Distribution format: tar.gzp><p id="sp000050">Programming language: Mathematica.p><p id="sp000055">Computer: All computers running Mathematica.p><p id="sp000060">Operating system: Operating systems running Mathematica.p><p id="sp000065">Classification: 4.4.p><p id="sp000070">Does the new version supersede the previous version?: No, it significantly extends the previous version.p><p id="sp000075">Nature of problem:p><p id="sp000080">Reduction of hypergeometric function pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301059&_mathId=si1.gif&_user=111111111&_pii=S0010465516301059&_rdoc=1&_issn=00104655&md5=5ab347796950cd505c439ec15d0d8212" title="Click to view the MathML source">F_Cpan>pan class="mathContainer hidden">pan class="mathCode">$F_C$pan>pan>pan> of three variables to a set of basis functions.p><p id="sp000085">Solution method:p><p id="sp000090">Differential reduction.p><p id="sp000095">Reasons for new version:p><p id="sp000100">The extension package allows the user to handle the Lauricella function pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301059&_mathId=si1.gif&_user=111111111&_pii=S0010465516301059&_rdoc=1&_issn=00104655&md5=5ab347796950cd505c439ec15d0d8212" title="Click to view the MathML source">F_Cpan>pan class="mathContainer hidden">pan class="mathCode">$F_C$pan>pan>pan> of three variables.p><p id="sp000105">Summary of revisions:p><p id="sp000110">The previous version goes unchanged.p><p id="sp000115">Running time:p><p id="sp000120">Depends on the complexity of the problem.