Mathematical constants | Real transcendental numbers

Lemniscate constant

In mathematics, the lemniscate constant ϖ is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter, analogous to the definition of π for the circle. It is closely related to the lemniscate elliptic functions and approximately equal to 2.62205755. The symbol ϖ is a cursive variant of π; see Pi § Variant pi. Gauss's constant, denoted by G, is equal to ϖ /π ≈ 0.8346268. John Todd named two more lemniscate constants, the first lemniscate constant A = ϖ/2 ≈ 1.3110287771 and the second lemniscate constant B = π/(2ϖ) ≈ 0.5990701173. Sometimes the quantities 2ϖ or A are referred to as the lemniscate constant. This article follows Gauss' definition for the lemniscate constant. (Wikipedia).

Lemniscate constant
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Transcendental number | Elliptic integral | Perimeter | Continued fraction | Derivative | Dirichlet beta function | Pentagonal number | Particular values of the gamma function | Infinite product | Euler's constant | Carl Friedrich Gauss | Gaussian integral | Square root of 2 | Lemniscate of Bernoulli | Arithmetic–geometric mean | Gamma function | Mathematics | Riemann zeta function | Machin-like formula | Basel problem | Pi | Viète's formula | Sine and cosine | Diameter | Beta function | Lemniscate elliptic functions | Algebraic independence | Wallis product | Theta function | Eisenstein series | Divisor function | Multiplicative inverse