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Euler (1738, 1753) considered the series s_a(x)=sum_(n=1)^infty[1/(1-a^n)product_(k=0)^(n-1)(1-xa^(-k))]. He showed that just like log_a(a^n)=n, s_a(a^n)=n for nonnegative ...

Let rho be a reciprocal difference. Then Thiele's interpolation formula is the continued fraction f(x)=f(x_1)+(x-x_1)/(rho(x_1,x_2)+)(x-x_2)/(rho_2(x_1,x_2,x_3)-f(x_1)+) ...

The transform inverting the sequence g(n)=sum_(d|n)f(d) (1) into f(n)=sum_(d|n)mu(d)g(n/d), (2) where the sums are over all possible integers d that divide n and mu(d) is the ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

The Gergonne line is Oldknow's (1996) term for the perspectrix of a contact triangle DeltaDEF and its reference triangle DeltaABC. It is determined by the Nobbs points D^', ...

The quartic formula is a name sometimes given to one of the related explicit formulas for the four roots z_1, ..., z_4 of an arbitrary quartic equation with real coefficients ...

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

A formula which transforms a given coordinate system by rotating it through a counterclockwise angle Phi about an axis n^^. Referring to the above figure (Goldstein 1980), ...

The orthocentroidal circle of a triangle DeltaABC is a central circle having the segment joining the triangle centroid G and orthocenter H of DeltaABC as its diameter ...

A sequence s_n^((lambda))(x)=[h(t)]^lambdas_n(x), where s_n(x) is a Sheffer sequence, h(t) is invertible, and lambda ranges over the real numbers is called a Steffensen ...