Sierpiński's constant

The Sierpiński constant is a mathematical constant named after the Polish mathematician Waclaw Sierpiński. It may be defined, inter alia, by the following expression:

The number of representations of is in the form of integers and in compliance with the order, the county number and ln is the natural logarithm.

Forms of representation

An explicit expression for the constant Sierpiński

With the Euler - Mascheroni constant, and the gamma function. Due to the relation

Gives the alternative representation

The decimal expansion of

RN ( k ) function

( Sequence A004018 in OEIS ).

The Sierpiński constant occurs in the study of the asymptotics of ( known in English as Sum of Squares designated ) function

For the case n = 2 (about to the case n = 4 is what the set of Jacobi ).

For example, = 0, since the number does 3 not written as the sum of two square numbers, while = 8, because 13 can be formed as the sum of the square numbers 9 and 4 in two different orders, and, each in four sign combinations.