Search results

Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually written with the symbols sl and cl (sometimes...

Hyperbolic function Lemniscate elliptic functions Law of sines List of periodic functions List of trigonometric identities Madhava series Madhava's sine table...

functions in 1797, the lemniscate elliptic functions in particular, but his work was published much later. There are twelve Jacobi elliptic functions...

(complexity), a class of computational complexity sl (elliptic function), sine lemniscate function Special linear group in mathematics, denoted SLn or SL(n)...

mathematics, the lemniscate constant ϖ is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter...

arises from integrals of purely algebraic functions. In particular, the arc lengths of ellipses and of the lemniscate, which are curves defined by algebraic...

a^{-1}(x)=\sin x} . So the sine function is an inverse function of an integral function. Elliptic functions are the inverse functions of elliptic integrals...

In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2c from each other as the...

Weierstrass's elliptic functions Lemniscate elliptic functions Theta functions Neville theta functions Modular lambda function Closely related are the modular...

trigonometric functions sine and cosine and the Jacobi elliptic functions sn and cn; Göran Dillner described them earlier in 1873. The functions sm and cm...

periodic function with just one zero. Elliptic function Abel elliptic functions Jacobi elliptic functions Weierstrass elliptic functions Lemniscate elliptic...

congruent to 1 mod 4 φ(z) = sl((1 – i)ωz) where sl is the sine lemniscate function, an elliptic function. χ is the mth power residue symbol in K with respect...

{\displaystyle \operatorname {sl} } is the lemniscate sine and ϖ {\displaystyle \varpi } is the lemniscate constant. The function λ ∗ ( x ) {\displaystyle \lambda...

{2}}\,\varpi {\bigr )}} With the letter ϖ {\displaystyle \varpi } the Lemniscate constant is represented. Note that the following modular identities hold:...

curve which generates each of them is expressed using cosine functions rather than sine functions. x = cos ⁡ ( t ) , y = cos ⁡ ( N t ) {\displaystyle x=\cos(t)...

Chen: Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions. Universität Henan, China, 2016. Minjie Wei, Yue He and...

– trigonometric identities for multiple distinct angles The Lemniscate elliptic functions, sinlem and coslem The Pythagorean theorem in non-Euclidean...

Lissajous-toric knot onto the x-y-plane is a Lissajous curve. Replacing the sine and cosine functions in the parametrization by a triangle wave transforms a Lissajous-toric...

{\displaystyle y=1/x} is a rectangular hyperbola. Using the hyperbolic sine and cosine functions cosh , sinh {\displaystyle \cosh ,\sinh } , a parametric representation...

converted to the Cartesian coordinates x and y by using the trigonometric functions sine and cosine: x = r cos ⁡ φ , y = r sin ⁡ φ . {\displaystyle {\begin{aligned}x&=r\cos...