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Experimental Mathematics Volume 3, 1994 - Issue 4
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Original Articles

On the Evaluation of Euler Sums

Richard E. Crandall Center for Advanced Computation, Reed College, Portland, OR, 97202 E-mail: [email protected]
&
Joe P. Buhler Department of Mathematics, Reed College, Portland, OR, 97202 E-mail: [email protected]
Pages 275-285 | Published online: 03 Apr 2012

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Karl Dilcher. (2021) Analytic Continuations of Character and Alternating Tornheim Zeta Functions. The American Mathematical Monthly 128:9, pages 780-795.
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Djurdje Cvijović. (2008) Closed-form evaluation of some families of cotangent and cosecant integrals. Integral Transforms and Special Functions 19:2, pages 147-155.
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Jonathan M. Borwein. (2008) Hilbert's Inequality and Witten's Zeta-Function. The American Mathematical Monthly 115:2, pages 125-137.
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RichardE. Crandall. (1999) New Representations for the Madelung Constant. Experimental Mathematics 8:4, pages 367-379.
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Philippe Flajolet & Bruno Salvy. (1998) Euler Sums and Contour Integral Representations. Experimental Mathematics 7:1, pages 15-35.
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Articles from other publishers (38)

Masato Kobayashi. (2023) From basel problem to multiple zeta values. The Journal of Analysis.
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Levent Kargın, Mümün Can, Ayhan Dil & Mehmet Cenkci. (2021) On Evaluations of Euler-Type Sums of Hyperharmonic Numbers. Bulletin of the Malaysian Mathematical Sciences Society 45:1, pages 113-131.
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Anthony Sofo & Amrik Singh Nimbran. (2019) Euler Sums and Integral Connections. Mathematics 7:9, pages 833.
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Jichao Zhang & Ce Xu. (2019) On some explicit evaluations of nonlinear Euler sums. Lithuanian Mathematical Journal 59:2, pages 261-275.
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Ce Xu. (2018) Some evaluation of cubic Euler sums. Journal of Mathematical Analysis and Applications 466:1, pages 789-805.
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Anthony Sofo. 2018. Mathematical Analysis and Applications. Mathematical Analysis and Applications 631 659 .
Jonathan M. Borwein & Karl Dilcher. (2017) Derivatives and fast evaluation of the Tornheim zeta function. The Ramanujan Journal 45:2, pages 413-432.
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Chung-Yie Chang. (2016) Shuffle Product Formulas of Two Multiples of Height-one Multiple Zeta Values. Taiwanese Journal of Mathematics 20:1.
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David H. Bailey & Jonathan M. BorweinDavid H. Bailey, Peter B. Borwein & Simon Plouffe. 2016. Pi: The Next Generation. Pi: The Next Generation 219 231 .
Minking Eie, Wen-Chin Liaw & Chuan-Sheng Wei. (2015) Double weighted sum formulas of multiple zeta values. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 85:1, pages 23-41.
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Minking Eie & Chuan-Sheng Wei. (2013) Generalizations of Euler decomposition and their applications. Journal of Number Theory 133:8, pages 2475-2495.
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István Mező. (2013) Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions. Open Mathematics 11:5.
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Minking Eie & Chuan-Sheng Wei. (2012) Evaluations of some quadruple Euler sums of even weight. Functiones et Approximatio Commentarii Mathematici 46:1.
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. 2012. Zeta and q-Zeta Functions and Associated Series and Integrals. Zeta and q-Zeta Functions and Associated Series and Integrals 603 657 .
Minking Eie & Wen-Chin Liaw. (2009) Double Euler Sums on Hurwitz Zeta Functions. Rocky Mountain Journal of Mathematics 39:6.
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Minking Eie, Wen-Chin Liaw & Yao Lin Ong. (2009) A restricted sum formula among multiple zeta values. Journal of Number Theory 129:4, pages 908-921.
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Djurdje Cvijović & H.M. Srivastava. (2009) Evaluations of some classes of the trigonometric moment integrals. Journal of Mathematical Analysis and Applications 351:1, pages 244-256.
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Ankur Basu. (2008) A new method in the study of Euler sums. The Ramanujan Journal 16:1, pages 7-24.
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Yao Lin Ong & Minking Eie. (2008) On Recurrence Relations for the Extensions of Euler Sums. Rocky Mountain Journal of Mathematics 38:1.
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JIANQIANG ZHAO. (2011) WOLSTENHOLME TYPE THEOREM FOR MULTIPLE HARMONIC SUMS. International Journal of Number Theory 04:01, pages 73-106.
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JONATHAN M. BORWEIN & DAVID M. BRADLEY. (2011) THIRTY-TWO GOLDBACH VARIATIONS. International Journal of Number Theory 02:01, pages 65-103.
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Kwang-Wu Chen & Minking Eie. (2006) Explicit evaluations of extended Euler sums. Journal of Number Theory 117:1, pages 31-52.
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Olivier Espinosa & Victor H. Moll. (2006) The evaluation of Tornheim double sums, Part 1. Journal of Number Theory 116:1, pages 200-229.
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MINKING EIEYAO LIN ONGFU YAO YANG. (2012) EVALUATING DOUBLE EULER SUMS OVER RATIONALLY DEFORMED SIMPLICES. International Journal of Number Theory 01:03, pages 439-458.
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Junesang Choi & H. M. Srivastava. (2005) Explicit Evaluation of Euler and Related Sums. The Ramanujan Journal 10:1, pages 51-70.
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MINKING EIEWEN-CHIN LIAWFU-YAO YANG. (2012) ON EVALUATION OF GENERALIZED EULER SUMS OF EVEN WEIGHT. International Journal of Number Theory 01:02, pages 225-242.
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Robert J. Petrella & Martin Karplus. (2005) Electrostatic energies and forces computed without explicit interparticle interactions: A linear time complexity formulation. Journal of Computational Chemistry 26:8, pages 755-787.
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Jens Vollinga & Stefan Weinzierl. (2005) Numerical evaluation of multiple polylogarithms. Computer Physics Communications 167:3, pages 177-194.
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Lennart Berggren, Jonathan Borwein & Peter BorweinDavid Bailey, Peter Borwein & Simon Plouffe. 2004. Pi: A Source Book. Pi: A Source Book 663 676 .
Richard K. GuyRichard K. Guy. 2004. Unsolved Problems in Number Theory. Unsolved Problems in Number Theory 365 404 .
A.I. Davydychev & M.Yu. Kalmykov. (2001) New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams. Nuclear Physics B 605:1-3, pages 266-318.
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Jonathan Borwein, David Bradley, David Broadhurst & Petr Lisoněk. (2000) Special values of multiple polylogarithms. Transactions of the American Mathematical Society 353:3, pages 907-941.
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Jonathan M. Borwein, David M. Bradley & Richard E. Crandall. (2000) Computational strategies for the Riemann zeta function. Journal of Computational and Applied Mathematics 121:1-2, pages 247-296.
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Lennart Berggren, Jonathan Borwein & Peter BorweinDavid Bailey, Peter Borwein & Simon Plouffe. 2000. Pi: A Source Book. Pi: A Source Book 663 676 .
Richard Crandall. (1998) Fast evaluation of multiple zeta sums. Mathematics of Computation 67:223, pages 1163-1172.
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David Bailey, Peter Borwein & Simon Plouffe. (1997) On the rapid computation of various polylogarithmic constants. Mathematics of Computation 66:218, pages 903-913.
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Victor Adamchik. (1997) On Stirling numbers and Euler sums. Journal of Computational and Applied Mathematics 79:1, pages 119-130.
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Lennart Berggren, Jonathan Borwein & Peter BorweinDavid Bailey, Peter Borwein & Simon Plouffe. 1997. Pi: A Source Book. Pi: A Source Book 663 676 .

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