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Orthogonal contravariant and covariant satisfy g_(ik)g^(ij)=delta_k^j, where delta_j^k is the Kronecker delta.

A tensor g whose discriminant satisfies g=g_(11)g_(22)-g_(12)^2>0.

A quantity which transforms like a tensor except for a scalar factor of a Jacobian.

The tensor defined by T^l_(jk)=-(Gamma^l_(jk)-Gamma^l_(kj)), where Gamma^l_(jk) are Christoffel symbols of the first kind.

Let f be an entire function of finite order lambda and {a_j} the zeros of f, listed with multiplicity, then the rank p of f is defined as the least positive integer such that ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

Any entire analytic function whose range omits two points must be a constant function. Of course, an entire function that omits a single point from its range need not be a ...

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)).

An anti-analytic function is a function f satisfying the condition (df)/(dz)=0. (1) Using the result ...

A Bergman kernel is a function of a complex variable with the "reproducing kernel" property defined for any domain in which there exist nonzero analytic functions of class ...