Unsolvability of the Pell minus-equation for certain odd discriminants
Gerhard A. Bachmaier (2007)
Acta Arithmetica
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Gerhard A. Bachmaier (2007)
Acta Arithmetica
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Xiquan Liang, Ling Tang, Xichun Jiang (2011)
Formalized Mathematics
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In this article, we give some important theorems of forward difference, backward difference, central difference and difference quotient and forward difference, backward difference, central difference and difference quotient formulas of some special functions.
Bo Li, Yanping Zhuang, Yanhong Men, Xiquan Liang (2009)
Formalized Mathematics
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In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, the hyperbolic function and the polynomial function [3].MML identifier: INTEGR11, version: 7.11.01 4.117.1046
Bo Li, Yanping Zhuang, Bing Xie, Pan Wang (2009)
Formalized Mathematics
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In this article, we give several integrability formulas of some functions including the trigonometric function and the index function [3]. We also give the definitions of the orthogonal polynomial and norm function, and some of their important properties [19].MML identifier: INTEGRA9, version: 7.11.01 4.117.1046
Noboru Endou, Yasunari Shidama, Keiko Narita (2008)
Formalized Mathematics
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The goal of this article is to prove Egoroff's Theorem [13]. However, there are not enough theorems related to sequence of measurable functions in Mizar Mathematical Library. So we proved many theorems about them. At the end of this article, we showed Egoroff's theorem.MML identifier: MESFUNC8, version: 7.8.10 4.100.1011
Fuguo Ge, Bing Xie (2008)
Formalized Mathematics
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In this article, we prove a series of differentiation identities [2] involving the arctan and arccot functions and specific combinations of special functions including trigonometric and exponential functions.MML identifier: FDIFF 11, version: 7.10.01 4.111.1036
R. Tosic (1972)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Junjie Zhao, Xiquan Liang, Li Yan (2008)
Formalized Mathematics
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In this paper, we proved some basic properties of higher differentiation, and higher differentiation formulas of special functions [4].MML identifier: HFDIFF 1, version: 7.8.10 4.100.1011
Bo Li, Na Ma (2010)
Formalized Mathematics
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In this article, we give several differentiation and integrability formulas of composite trigonometric function.
Bo Li, Yanping Zhuang, Xiquan Liang (2008)
Formalized Mathematics
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In this article, we give some important properties of forward difference, backward difference, central difference and difference quotient and forward difference, backward difference, central difference and difference quotient formulas of some special functions [11].MML identifier: DIFF 2, version: 7.8.09 4.97.1001
Haryono Tandra (2013)
The Teaching of Mathematics
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Đurđica Takači, Dragoslav Herceg, Radivoje Stojković (2005)
The Teaching of Mathematics
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Xiquan Liang, Ling Tang (2010)
Formalized Mathematics
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In this article, we give some important theorems of forward difference, backward difference, central difference and difference quotient and forward difference, backward difference, central difference and difference quotient formulas of some special functions.