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A strong pseudoprime to a base a is an odd composite number n with n-1=d·2^s (for d odd) for which either a^d=1 (mod n) (1) or a^(d·2^r)=-1 (mod n) (2) for some r=0, 1, ..., ...

The tangent function is defined by tanx=(sinx)/(cosx), (1) where sinx is the sine function and cosx is the cosine function. The notation tgx is sometimes also used ...

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 Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse sequence (Allouche and Cosnard 2000), is one of a number of related sequences of numbers ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

The xi-function is the function xi(z) = 1/2z(z-1)(Gamma(1/2z))/(pi^(z/2))zeta(z) (1) = ((z-1)Gamma(1/2z+1)zeta(z))/(sqrt(pi^z)), (2) where zeta(z) is the Riemann zeta ...

The (unilateral) Z-transform of a sequence {a_k}_(k=0)^infty is defined as Z[{a_k}_(k=0)^infty](z)=sum_(k=0)^infty(a_k)/(z^k). (1) This definition is implemented in the ...

The (unilateral) Z-transform of a sequence {a_k}_(k=0)^infty is defined as Z[{a_k}_(k=0)^infty](z)=sum_(k=0)^infty(a_k)/(z^k). (1) This definition is implemented in the ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...