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Functions That Do Not Have Unique ValuesOrthogonal Polynomials

3.2.8 Mathematical Constants

Mathematical constants.

Euler's constant EulerGamma is given by the limit . It appears in many integrals, and asymptotic formulas. It is sometimes known as the Euler-Mascheroni constant, and denoted .

Catalan's constant Catalan is given by the sum . It often appears in asymptotic estimates of combinatorial functions.

Khinchin's constant Khinchin (sometimes called Khintchine's constant) is given by . It gives the geometric mean of the terms in the continued fraction representation for a typical real number.

Glaisher's constant Glaisher (sometimes called the Glaisher-Kinkelin constant) satisfies , where is the Riemann zeta function. It appears in various sums and integrals, particularly those involving gamma and zeta functions.

Mathematical constants can be evaluated to arbitrary precision.

In[1]:= N[EulerGamma, 40]

Out[1]=

Exact computations can also be done with them.

In[2]:= IntegerPart[GoldenRatio^100]

Out[2]=

Functions That Do Not Have Unique ValuesOrthogonal Polynomials