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The length of the largest-sized square contained within the Ferrers diagram of a partition. Its size can be determined using DurfeeSquare[f] in the Wolfram Language package ...

The exsecant is a little-used trigonometric function defined by exsec(x)=secx-1, (1) where secx is the secant. The exsecant can be extended to the complex plane as ...

The W-polynomials obtained by setting p(x)=3x and q(x)=-2 in the Lucas polynomial sequence. The first few Fermat polynomials are F_1(x) = 1 (1) F_2(x) = 3x (2) F_3(x) = ...

A distribution which arises in the study of half-integer spin particles in physics, P(k)=(k^s)/(e^(k-mu)+1). (1) Its integral is given by int_0^infty(k^sdk)/(e^(k-mu)+1) = ...

Let r be the correlation coefficient. Then defining z^'=tanh^(-1)r (1) zeta=tanh^(-1)rho, (2) gives sigma_(z^') = (N-3)^(-1/2) (3) var(z^') = 1/n+(4-rho^2)/(2n^2)+... (4) ...

The flattening of a spheroid (also called oblateness) is denoted epsilon or f (Snyder 1987, p. 13). It is defined as epsilon={(a-c)/a=1-c/a oblate; (c-a)/a=c/a-1 prolate, (1) ...

Given a semicircular hump f(x) = sqrt(L^2-(x-L)^2) (1) = sqrt((2L-x)x), (2) the Fourier coefficients are a_0 = 1/2piL (3) a_n = ((-1)^nLJ_1(npi))/n (4) b_n = 0, (5) where ...

F_x[cos(2pik_0x)](k) = int_(-infty)^inftye^(-2piikx)((e^(2piik_0x)+e^(-2piik_0x))/2)dx (1) = 1/2int_(-infty)^infty[e^(-2pii(k-k_0)x)+e^(-2pii(k+k_0)x)]dx (2) = ...

F_x[sin(2pik_0x)](k) = int_(-infty)^inftye^(-2piikx)((e^(2piik_0x)-e^(-2piik_0x))/(2i))dx (1) = 1/2iint_(-infty)^infty[-e^(-2pii(k-k_0)x)+e^(-2pii(k+k_0)x)]dx (2) = ...

Let C_(L,M) be a Padé approximant. Then C_((L+1)/M)S_((L-1)/M)-C_(L/(M+1))S_(L/(M+1)) = C_(L/M)S_(L/M) (1) C_(L/(M+1))S_((L+1)/M)-C_((L+1)/M)S_(L/(M+1)) = ...