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Home > Euler-Mascheroni constant

Intriguingly, the constant is also given by the integral:

Its value is approximately

γ ≈ 0.577215664901532860606512090082402431042159335 9399235988057672348848677267776646709369470632917467495...

It is not known whether γ is a rational number or not. However, continued fraction analysis shows that if γ is rational, its denominator has more than 10,000 digits.

The Euler-Mascheroni constant appears, among other places, in:

• a product formula for the gamma function
• calculations of the digamma function
• calculation of the Meissel-Mertens constant
• expressions involving the exponential integral

It is named for the mathematicians Leonhard Euler and Lorenzo Mascheroni.

External link

• Euler-Mascheroni constant at MathWorld

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Topics: Euler-Mascheroni Constant Gamma Mathematical Number Function...

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Euler's formulaThis article is about the Euler's formula in complex analysis . There is also Euler's formula which is related to the Euler characteristic in algebraic topology. Euler's formula named after Leonhard Euler, is a mathematical formula in the subfield of comp Euler-Maclaurin formulaIn mathematics, the Euler-Maclaurin formula provides a powerful connection between integrals (see calculus) and sums. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the Euler's conjectureEuler's conjecture is a conjecture related to Fermat's last theorem which was proposed by Leonhard Euler in 1769. It states that for every integer n greater than 2, the sum of n 1 n th powers of positive integers cannot itself be an n th power. The conjec Euler's identityIn mathematics, Euler's identity a special case of Euler's formula, is the following: : The equation appears in Leonhard Euler's Introduction published in Lausanne in 1748. In this equation, e is the base of the natural logarithm, is the imaginary unit (a Euler numberThe Euler numbers are a sequence E of integers defined by the following Taylor series expansion: : (Note that e the base of the natural logarithm, is also occasionally called Euler's number as is the Euler characteristic. The odd-indexed Euler numbers are Euler's totient functionIn number theory, the totient φ n of a positive integer n is defined to be the number of positive integers less than or equal to n and coprime to n''. For example, φ(8) 4 since the four numbers 1, 3, 5 and 7 are coprime to 8. The function φ so Euler's theorem Euler-Jacobi pseudoprime Euler's criterion Euler characteristic Euler-Mascheroni constant Euler's line Euler prime Euler's four-square identity Euler pseudoprime