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_2F_1(a,b;c;1)=((c-b)_(-a))/((c)_(-a))=(Gamma(c)Gamma(c-a-b))/(Gamma(c-a)Gamma(c-b)) for R[c-a-b]>0, where _2F_1(a,b;c;x) is a (Gauss) hypergeometric function. If a is a ...

An elliptic integral is an integral of the form int(A(x)+B(x)sqrt(S(x)))/(C(x)+D(x)sqrt(S(x)))dx, (1) or int(A(x)dx)/(B(x)sqrt(S(x))), (2) where A(x), B(x), C(x), and D(x) ...

The duplication formula for Rogers L-function follows from Abel's functional equation and is given by 1/2L(x^2)=L(x)-L(x/(1+x)).

A convex body in Euclidean space that is centrally symmetric with center at the origin is determined among all such bodies by its brightness function (the volume of each ...

For a measurable function mu, the Beltrami differential equation is given by f_(z^_)=muf_z, where f_z is a partial derivative and z^_ denotes the complex conjugate of z.

A mathematical object (such as a set or function) is said to bounded if it possesses a bound, i.e., a value which all members of the set, functions, etc., are less than.

If a and n are relatively prime so that the greatest common divisor GCD(a,n)=1, then a^(lambda(n))=1 (mod n), where lambda is the Carmichael function.

An expansion based on the roots of x^(-n)[xJ_n^'(x)+HJ_n(x)]=0, where J_n(x) is a Bessel function of the first kind, is called a Dini expansion.

Define g(k) as the quantity appearing in Waring's problem, then Euler conjectured that g(k)=2^k+|_(3/2)^k_|-2, where |_x_| is the floor function.

A 1-form w is said to be exact in a region R if there is a function f that is defined and of class C^1 (i.e., is once continuously differentiable in R) and such that df=w.