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In mathematics, Itô's lemma or Itô's formula (also called the Itô–Doeblin formula, especially in the French literature) is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart of the chain rule.
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...
He was the first Chinese mathematician to calculate π=3.1416 with his π algorithm. He discovered the usage of Cavalieri's principle to find an accurate formula for the volume of a cylinder, and also developed elements of the infinitesimal calculus during the 3rd century CE. fraction interpolation for pi
The mathematical derivation for the Eötvös effect for motion along the Equator explains the factor 2 in the first term of the Eötvös correction formula. What remains to be explained is the cosine factor. Because of its rotation, the Earth is not spherical in shape, there is an Equatorial bulge. The force of gravity is directed towards the ...
Using MFDR and formulas above, an adjusted MFDR (or AFDR) is the minimum of the mean for m dependent tests, i.e., () = (+) [ +] +. Another way to address dependence is by bootstrapping and rerandomization.
Esotropia (from Greek eso 'inward' and trope 'a turning' [1]) is a form of strabismus in which one or both eyes turn inward. The condition can be constantly present, or occur intermittently, and can give the affected individual a "cross-eyed" appearance. [2]
These three results coincide with gamma correction of the bottom layer with γ=2 (for top black), unchanged bottom layer (or, what is the same, γ=1; for top neutral gray), and γ=0.5 (for top white). The formula used by Photoshop as of 2012 has a discontinuity of local contrast, and other formulas correct it. Photoshop's formula is: [6]
The best known approximations to π dating to before the Common Era were accurate to two decimal places; this was improved upon in Chinese mathematics in particular by the mid-first millennium, to an accuracy of seven decimal places.