Central binomial sums, multiple Clausen values, and zeta values
Borwein, Jonathan Michael ; Broadhurst, David J. ; Kamnitzer, Joel
Experiment. Math., Tome 10 (2001) no. 3, p. 25-34 / Harvested from Project Euclid
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We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apery sums). The study of nonalternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio.
Publié le : 2001-05-14
Classification:  binomial sums,  multiple zeta values,  log-sine integrals,  Clausen's function,  multiple Clausen values,  polylogarithms,  Apéry sums,  11Mxx,  05Axx,  11Bxx,  33Bxx 
@article{999188418,
     author = {Borwein, Jonathan Michael and Broadhurst, David J. and Kamnitzer, Joel},
     title = {Central binomial sums, multiple Clausen values, and zeta values},
     journal = {Experiment. Math.},
     volume = {10},
     number = {3},
     year = {2001},
     pages = { 25-34},
     language = {en},
     url = {http://dml.mathdoc.fr/item/999188418}
}

Borwein, Jonathan Michael; Broadhurst, David J.; Kamnitzer, Joel. Central binomial sums, multiple Clausen values, and zeta values. Experiment. Math., Tome 10 (2001) no. 3, pp.  25-34. http://gdmltest.u-ga.fr/item/999188418/