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For R[z]>0, where J_nu(z) is a Bessel function of the first kind.

Let a general theta function be defined as T(x,q)=sum_(n=-infty)^inftyx^nq^(n^2), then

The set of all Schwartz functions is called a Schwartz space and is denoted S(R^n). If C_0^infty(R^n) denotes the set of smooth functions of compact support on R^n, then this ...

The Schwarzian derivative is defined by D_(Schwarzian)=(f^(''')(x))/(f^'(x))-3/2[(f^('')(x))/(f^'(x))]^2. The Feigenbaum constant is universal for one-dimensional maps if its ...

A Cantor set C in R^3 is said to be scrawny if for each neighborhood U of an arbitrary point p in C, there is a neighborhood V of p such that every map f:S^1->V subset C ...

D = f_(xx)f_(yy)-f_(xy)f_(yx) (1) = f_(xx)f_(yy)-f_(xy)^2, (2) where f_(ij) are partial derivatives.

The mathematical object kappa which controls the rate of geodesic deviation.

In random number computation, a seed is an initial number used as the starting point in a random number generating algorithm. In a dynamical system, a seed is a starting ...

X subset= R^n is semianalytic if, for all x in R^n, there is an open neighborhood U of x such that X intersection U is a finite Boolean combination of sets {x^_ in ...

A phase curve (i.e., an invariant manifold) which meets a hyperbolic fixed point (i.e., an intersection of a stable and an unstable invariant manifold) or connects the ...