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Let m and m+h be two consecutive critical indices of f and let F be (m+h)-normal. If the polynomials p^~_k^((n)) are defined by p^~_0^((n))(u) = 1 (1) p^~_(k+1)^((n))(u) = ...

A function tau(n) related to the divisor function sigma_k(n), also sometimes called Ramanujan's tau function. It is defined via the Fourier series of the modular discriminant ...

The prime zeta function P(s)=sum_(p)1/(p^s), (1) where the sum is taken over primes is a generalization of the Riemann zeta function zeta(s)=sum_(k=1)^infty1/(k^s), (2) where ...

The number of degrees of freedom in a problem, distribution, etc., is the number of parameters which may be independently varied.

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

An idealized coin consists of a circular disk of zero thickness which, when thrown in the air and allowed to fall, will rest with either side face up ("heads" H or "tails" T) ...

The Mangoldt function is the function defined by Lambda(n)={lnp if n=p^k for p a prime; 0 otherwise, (1) sometimes also called the lambda function. exp(Lambda(n)) has the ...

A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...

The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with very deep ...

Critical damping is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0, (1) in which D=beta^2-4omega_0^2=0, (2) where beta is the damping constant. ...