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36 results on '"Yan, Qinglun"'

2. Extensions of two $q$-Gosper identities with an extra integer parameter

Author

Wei, Chuanan and Yan, Qinglun

Subjects
Mathematics - Combinatorics, Mathematics - Classical Analysis and ODEs
Abstract

According to the method of series rearrangement, we establish the extensions of two $q$-Gosper identities with an extra integer parameter. The limiting cases of them produce the generalizations of Gosper's two $_3F_2(\frac{3}{4})$-series identities with an additional integer parameter. Meanwhile, several related results are also given.

Published
2014

3. Generalizations of Ramanujan's reciprocity formula and the Askey-Wilson integral

Author

Wei, Chuanan, Wang, Xiaoxia, and Yan, Qinglun

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

By using two known transformation formulas for basic hypergeometric series, we establish a direct extension of Bailey's $_6\psi_6$-series identity. Subsequently, it and Milne's identity are employed to drive multi-variable generalizations of Ramanujan's reciprocity formula. Then we utilize also Milne's identity to deduce a multi-variable generalization of the Askey-Wilson integral.

Published
2013

4. A family of summation formulas involving generalized harmonic numbers

Author

Wei, Chuanan, Yan, Qinglun, and Gong, Dianxuan

Subjects
Mathematics - Combinatorics, Mathematics - Number Theory
Abstract

Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.

Published
2012

5. A class of summation formulas on generalized harmonic numbers

Author

Wei, Chuanan, Gong, Dianxuan, and Yan, Qinglun

Subjects
Mathematics - Combinatorics, Mathematics - Number Theory
Abstract

Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers., Comment: This paper has been withdrawn by the author because that the main results of it are trivial

Published
2012

6. A short proof for Dougall's $_2H_2$-series identity

Author

Wei, Chuanan, Yan, Qinglun, and Li, Jianbo

Subjects
Mathematics - Combinatorics, Primary 05A19 and Secondary 33C20
Abstract

According to Chen and Fu's method, we offer a short proof for Dougall's $_2H_2$-series identity.

Published
2011

9. Interior Point Algorithm for Constrained Sequential Max-Min Problems

Author

Fan, Xiaona, Yan, Qinglun, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Zhu, Rongbo, editor, Zhang, Yanchun, editor, Liu, Baoxiang, editor, and Liu, Chunfeng, editor

Published
2010
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10. Aggregate Homotopy Method for Solving the Nonlinear Complementarity Problem

Author

Fan, Xiaona, Yan, Qinglun, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Zhu, Rongbo, editor, Zhang, Yanchun, editor, Liu, Baoxiang, editor, and Liu, Chunfeng, editor

Published
2010
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22. Solving system of inequalities via a smoothing homotopy method.

Author

Fan, Xiaona and Yan, Qinglun

Subjects
*SMOOTHING (Numerical analysis), *NONLINEAR systems, *SMOOTHNESS of functions, *MATHEMATICAL equivalence
Abstract

In this paper, the system of nonlinear inequalities is considered. The problem is approximated by the parameterized smooth equations which is formed by Chen-Harker-Kanzow-Smale smoothing function. A smoothing homotopy method is proposed to solve the system of smooth equations. For almost all initial points in Euclidean space, the existence and convergence of the homotopy path is proved under certain weaker condition without assumption of the monotonicity. The numerical results illustrate that the method is effective. [ABSTRACT FROM AUTHOR]

Published
2019
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35. Telescoping method, derivative operators and harmonic number identities.

Author

Wei, Chuanan, Gong, Dianxuan, and Yan, Qinglun

Subjects
DERIVATIVES (Mathematics), OPERATOR theory, HARMONIC analysis (Mathematics), NUMBER theory, IDENTITIES (Mathematics), MATHEMATICAL analysis
Abstract

In terms of the telescoping method, a simple binomial sum is given. By applying the derivative operators to the equation just mentioned, we establish several general harmonic number identities including some known results. [ABSTRACT FROM PUBLISHER]

Published
2014
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36. Winquist’s identity and Ramanujan’s partition congruence p(11n+6)≡0(mod11)

Author

Chu, Wenchang and Yan, Qinglun

Abstract

By means of the difference equation on the modified Jacobi theta function, we review the proof of Winquist’s identity due to Kang [S.Y. Kang, A new proof Winquist’s identity, J. Combin. Theory (Series A) 78 (1997) 313–318]. Four related expansion formulae are examined and clarified equivalently in pairs. The recent double series representation for (q;q)∞10 due to Chan [S.H. Chan, Generalized lambert series identities, Proc. London Math. Soc. 91 (3) (2005) 598–622] is exemplified to prove the Ramanujan congruence modulo 11 on the partition function.

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