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If p>1, then Minkowski's integral inequality states that Similarly, if p>1 and a_k, b_k>0, then Minkowski's sum inequality states that [sum_(k=1)^n|a_k+b_k|^p]^(1/p) ...

In functional analysis, the term "Poincaré-Friedrichs inequality" is a term used to describe inequalities which are qualitatively similar to the classical Poincaré Inequality ...

Consider the sum (1) where the x_js are nonnegative and the denominators are positive. Shapiro (1954) asked if f_n(x_1,x_2,...,x_n)>=1/2n (2) for all n. It turns out ...

If P is a pedal point inside a triangle DeltaABC, and P_A, P_B, and P_C are the feet of the perpendiculars from P upon the respective sides BC, CA, and AB, then ...

The Gini coefficient (or Gini ratio) G is a summary statistic of the Lorenz curve and a measure of inequality in a population. The Gini coefficient is most easily calculated ...

Simpson's rule is a Newton-Cotes formula for approximating the integral of a function f using quadratic polynomials (i.e., parabolic arcs instead of the straight line ...

Roman (1984, p. 2) describes umbral calculus as the study of the class of Sheffer sequences. Umbral calculus provides a formalism for the systematic derivation and ...

Consider the Euler product zeta(s)=product_(k=1)^infty1/(1-1/(p_k^s)), (1) where zeta(s) is the Riemann zeta function and p_k is the kth prime. zeta(1)=infty, but taking the ...

Since |(a+ib)(c+id)| = |a+ib||c+di| (1) |(ac-bd)+i(bc+ad)| = sqrt(a^2+b^2)sqrt(c^2+d^2), (2) it follows that (a^2+b^2)(c^2+d^2) = (ac-bd)^2+(bc+ad)^2 (3) = e^2+f^2. (4) This ...

For P and Q polynomials in n variables, |P·Q|_2^2=sum_(i_1,...,i_n>=0)(|P^((i_1,...,i_n))(D_1,...,D_n)Q(x_1,...,x_n)|_2^2)/(i_1!...i_n!), where D_i=partial/partialx_i, |X|_2 ...