Taniguchi's Constant

Taniguchi's constant is defined as


(OEIS A175639), where the product is over the primes p. Taking the logarithm, expand the sum about infinity, and then summing the terms gives a "closed" form as


where P(n) is the prime zeta function and the c_ns are rational numbers given as the coefficients of p^(-1) in the series


See also

Artin's Constant, Barban's Constant, Feller-Tornier Constant, Heath-Brown-Moroz Constant, Murata's Constant, Prime Products, Prime Zeta Function, Quadratic Class Number Constant, Sarnak's Constant, Twin Primes Constant

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More things to try:


Finch, S. "Class Number Theory." May 6, 2005.Sloane, N. J. A. Sequence A175639 in "The On-Line Encyclopedia of Integer Sequences."Taniguchi, T. "A Mean Value Theorem for the Square of Class Number Times Regulator of Quadratic Extensions." 3 Jul 2006.

Cite this as:

Weisstein, Eric W. "Taniguchi's Constant." From MathWorld--A Wolfram Web Resource.

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