Abstract
A parameterized family of series representations for the numbers ζ(2m+1) is presented where m is a positive integer. Based on Clausen functions of higher order, several conventional results are improved and generalized; in particular, the rate of convergence can considerably be improved. The parameterized family is also applicable to represent the numbers β(2m) and to derive asymptotically finite representations for both ζ(2m+1) and β(2m).
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