Sierpiński's constant

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Sierpiński's constant is a mathematical constant usually denoted as K. One way of defining it is by limiting the expression:

where r2(k) is a number of representations of k as a sum of the form a2 + b2 for integer a and b.

It can be given in closed form as:

where is Gauss's constant and is the Euler-Mascheroni constant.

See also[edit]

External links[edit]

  • http://www.scenta.co.uk/tcaep/science/constant/details/sierpinskisconstant.xml[permanent dead link]
  • http://www.plouffe.fr/simon/constants/sierpinski.txt - Sierpiński's constant up to 2000th decimal digit.
  • Weisstein, Eric W. "Sierpinski Constant". MathWorld.
  • OEIS sequence A062089 (Decimal expansion of Sierpiński's constant)