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Cauchy's integral formula states that f(z_0)=1/(2pii)∮_gamma(f(z)dz)/(z-z_0), (1) where the integral is a contour integral along the contour gamma enclosing the point z_0. It ...

For R[mu+nu]>1, int_(-pi/2)^(pi/2)cos^(mu+nu-2)thetae^(itheta(mu-nu+2xi))dtheta=(piGamma(mu+nu-1))/(2^(mu+nu-2)Gamma(mu+xi)Gamma(nu-xi)), where Gamma(z) is the gamma function.

In mathematics, a formula is a fact, rule, or principle that is expressed in terms of mathematical symbols. Examples of formulas include equations, equalities, identities, ...

If f(z) is analytic in some simply connected region R, then ∮_gammaf(z)dz=0 (1) for any closed contour gamma completely contained in R. Writing z as z=x+iy (2) and f(z) as ...

The geometric mean is smaller than the arithmetic mean, (product_(i=1)^Nn_i)^(1/N)<=(sum_(i=1)^(N)n_i)/N, with equality in the cases (1) N=1 or (2) n_i=n_j for all i,j.

The Riemann-Siegel integral formula is the following representation of the xi-function xi(s) found in Riemann's Nachlass by Bessel-Hagen in 1926 (Siegel 1932; Edwards 2001, ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

Let sumu_k be a series with positive terms and let f(x) be the function that results when k is replaced by x in the formula for u_k. If f is decreasing and continuous for ...

The Cauchy remainder is a different form of the remainder term than the Lagrange remainder. The Cauchy remainder after n terms of the Taylor series for a function f(x) ...

Gregory's formula is a formula that allows a definite integral of a function to be expressed by its sum and differences, or its sum by its integral and difference (Jordan ...