Publication: Efficient Higher-Order Derivatives of the Hypergeometric Function
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Efficient Higher-Order Derivatives of the Hypergeometric Function

- incollection -
 

Author(s)
Isabelle Charpentier , Claude Dal Cappello , Jean Utke

Published in
Advances in Automatic Differentiation

Editor(s)
Christian H. Bischof, H. Martin Bücker, Paul D. Hovland, Uwe Naumann, J. Utke

Year
2008

Publisher
Springer

Abstract
Various physics applications involve the computation of the standard hypergeometric function 2F1 and its derivatives. Because it is not an intrinsic in the common programming languages, automatic differentiation tools will either differentiate through the code that computes 2F1 if that code is available or require the user to provide a hand-written derivative code. We present options for the derivative computation in the context of an ionization problem and compare the approach implemented in the Diamant library to standard methods.

Cross-References
Bischof2008AiA

AD Tools
Diamant, Rapsodia

AD Theory and Techniques
Higher Order, Taylor Arithmetic

BibTeX
@INCOLLECTION{
         Charpentier2008EHO,
       title = "Efficient Higher-Order Derivatives of the Hypergeometric Function",
       doi = "10.1007/978-3-540-68942-3_12",
       author = "Isabelle Charpentier and Claude Dal Cappello and Jean Utke",
       abstract = "Various physics applications involve the computation of the standard hypergeometric
         function 2F1 and its derivatives. Because it is not an intrinsic in the common programming
         languages, automatic differentiation tools will either differentiate through the code that computes
         2F1 if that code is available or require the user to provide a hand-written derivative code. We
         present options for the derivative computation in the context of an ionization problem and compare
         the approach implemented in the Diamant library to standard methods.",
       crossref = "Bischof2008AiA",
       pages = "127--137",
       booktitle = "Advances in Automatic Differentiation",
       publisher = "Springer",
       editor = "Christian H. Bischof and H. Martin B{\"u}cker and Paul D. Hovland and Uwe
         Naumann and J. Utke",
       isbn = "978-3-540-68935-5",
       issn = "1439-7358",
       year = "2008",
       ad_tools = "Diamant, Rapsodia",
       ad_theotech = "Higher Order, Taylor Arithmetic"
}


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