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Line 12  the Holonomic Gradient Descent Method  (HGD) </h1>
Line 12  the Holonomic Gradient Descent Method  (HGD) </h1>
   
 <h2> Papers  and Tutorials</h2>  <h2> Papers  and Tutorials</h2>
 <ol>  <ol>
   <li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
   Holonomic Gradient Method for Two Way Contingency Tables,
   <a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>
   <li> F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu,
   Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix
   (Title of the version 1: Holonomic Gradient Method for the Distribution Function of the Largest Root of Complex Non-central Wishart Matrices),
   <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
   <li> T.Koyama,
   An integral formula for the powered sum of the independent, identically and normally distributed random variables,
   <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
   <li> H.Hashiguchi, N.Takayama, A.Takemura,
   Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
   by Holonomic Gradient Method,
   <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
   
   <li> R.Vidunas, A.Takemura,
   Differential relations for the largest root distribution
   of complex non-central Wishart matrices,
   <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
   
   <li> S.Mano,
   The A-hypergeometric System Associated with the Rational Normal Curve and
   Exchangeable Structures,
   <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
   
   <li> M.Noro,
   System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
   <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
   
 <li> Y.Goto, K.Matsumoto,  <li> Y.Goto, K.Matsumoto,
 Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,  Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
 <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>  <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
Line 31  A-Hpergeometric Distributions and Newton Polytopes,
Line 60  A-Hpergeometric Distributions and Newton Polytopes,
 Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,  Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
 <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>  <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
   
   <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
   Exact ZF Analysis and Computer-Algebra-Aided Evaluation
   in Rank-1 LoS Rician Fading,
   <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
   
 <li> K.Ohara, N.Takayama,  <li> K.Ohara, N.Takayama,
 Pfaffian Systems of A-Hypergeometric Systems II ---  Pfaffian Systems of A-Hypergeometric Systems II ---
 Holonomic Gradient Method,  Holonomic Gradient Method,
Line 49  of noncentral chi-square random variables,
Line 83  of noncentral chi-square random variables,
 Contiguity relations of Lauricella's F_D revisited,  Contiguity relations of Lauricella's F_D revisited,
 <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>  <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
   
   <li>
   T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
   Software Packages for Holonomic Gradient Method,
   Mathematial Software --- ICMS 2014,
   4th International Conference, Proceedings.
   Edited by Hoon Hong and Chee Yap,
   Springer lecture notes in computer science 8592,
   706--712.
   <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
   DOI
   </a>
   
 <li>N.Marumo, T.Oaku, A.Takemura,  <li>N.Marumo, T.Oaku, A.Takemura,
 Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,  Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
 <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>  <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
Line 69  Holonomic Modules Associated with Multivariate Normal 
Line 115  Holonomic Modules Associated with Multivariate Normal 
 Pfaffian Systems of A-Hypergeometric Equations I,  Pfaffian Systems of A-Hypergeometric Equations I,
 Bases of Twisted Cohomology Groups,  Bases of Twisted Cohomology Groups,
 <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>  <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
 (major revision v2 of arxiv:1212.6103)  (major revision v2 of arxiv:1212.6103).
   Accepted version is at
   <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
   
 <li> <img src="./wakaba01.png" alt="Intro">  <li> <img src="./wakaba01.png" alt="Intro">
 <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">  <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
Line 156  equations.
Line 204  equations.
   
 <h2> Software Packages for HGM</h2>  <h2> Software Packages for HGM</h2>
   
 CRAN package <a href="https//cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).  <ul>
   <li>
   CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
   
 <br>  <li>
 Some software packages are experimental and temporary documents are found in  Some software packages are experimental and temporary documents are found in
 "asir-contrib manual" (auto-autogenerated part), or  "asir-contrib manual" (auto-autogenerated part), or
 "Experimental Functions in Asir", or "miscellaneous and other documents"  "Experimental Functions in Asir", or "miscellaneous and other documents"
Line 194  maximal Likehood estimates for the Fisher-Bingham dist
Line 244  maximal Likehood estimates for the Fisher-Bingham dist
 </ul>  </ul>
 </ol>  </ol>
   
   </ul>
   
 <h2> Programs to try examples of our papers </h2>  <h2> Programs to try examples of our papers </h2>
 <ol>  <ol>
 <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>  <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
 </ol>  </ol>
   
 <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.13 2016/02/05 21:42:46 takayama Exp $ </pre>  <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.24 2018/03/19 01:17:46 takayama Exp $ </pre>
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