THE SOLUTION OF THE PROBLEM OF INTEGRATION IN FINITE TERMS

Keywords

Exponentiation, Elementary function, Mathematics, Trigonometric functions, Algebra over a field

References

• Complex multiplication of Abelian varieties and its applications to number theory五郎 志村, 豊 谷山 — 1961
• Introduction to the Theory of Algebraic Numbers and FunctionsMartin Eichler — 1966
• The Integration of Functions of a Single VariableGodfrey Harold Hardy — 1906
• Diophantine Equations with Special Reference To Elliptic CurvesJ. W. S. Cassels — 1966
• The problem of integration in finite termsRobert H. Risch — 1969
• On the Birational Equivalence of Curves Under SpecializationWei-Liang Chow, Serge Lang — 1957
• Algebraic functionsGilbert Ames Bliss — 1933
• Traité des fonctions elliptiques et de leurs applicationsG. Halphen — 1888
• The Problem of Integration in Finite TermsRobert H. Risch — 1969

Cited by

• An Implementation of Karr's Summation Algorithm in MathematicaCarsten Schneider, J. Kepler — 1999
• The Relegation AlgorithmAndré Deprit, Jesúus Palacián, Étienne Deprit — 2001
• Fonctions holonomes en calcul formelFrédéric Chyzak — 1998
• Fourier series and integral transforms1998
• Intuition in formal proof : a novel framework for combining mathematical toolsLaura I. Meikle — 2014
• Some applications of differential-difference algebra to creative telescoping. (Quelques applications de l'algébre différentielle et aux différences pour le télescopage créatif)Shaoshi Chen — 2011
• Computer algebra systems: Issues and inquiriesWarren Page — 1990
• Galois Theory of Linear Differential EquationsMarius van der Put, Michael F. Singer — 2012
• Modern computer algebraJ. Gathen, Jürgen Gerhard — 2002
• ABSTRACTS (Amsterdam 78)Rüdiger Loos — 1977
• Computer Algebra: Past and FutureB. F. Caviness — 1985
• Towards a general theory of special functionsJoel Moses — 1972
• Intégration algorithmique des fonctions élémentairement transcendantes sur une courbe algébriqueJames H. Davenport — 1984
• Linear differential equations in exponential extensionsAnne Fredet — 2004
• Symbolic summation with radical expressionsManuel Kauers, Carsten Schneider — 2007
• Summation in Finite TermsMichael Karr — 1981
• MACSYMA from F to GRichard Pavelle, Paul S. Wang — 1985
• The integration of a class of special functions with the Risch algorithmJoel Moses — 1969
• On the implementation of a new algorithm for the computation of hyperelliptic integralsLaurent Bertrand — 1994
• Integration of algebraic functions: a simple heuristic for finding the logarithmic partManuel Kauers — 2008

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