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A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...

Catalan's constant is a constant that commonly appears in estimates of combinatorial functions and in certain classes of sums and definite integrals. It is usually denoted K ...

The Mittag-Leffler function (Mittag-Leffler 1903, 1905) is an entire function defined by the series E_alpha(z)=sum_(k=0)^infty(z^k)/(Gamma(alphak+1)) (1) for alpha>0. It is ...

Call a number of the form n^2-k a "near-square number." Numbers of the form n^2-5 for n=1, 2, ... are -4, -1, 4, 11, 20, 31, 44, 59, 76, 95, ... (OEIS A028875). These are ...

The odd graph O_n of order n is a graph having vertices given by the (n-1)-subsets of {1,...,2n-1} such that two vertices are connected by an edge iff the associated subsets ...

The Wythoff array is an interspersion array that can be constructed by beginning with the Fibonacci numbers {F_2,F_3,F_4,F_5,...} in the first row and then building up ...

Given a set of linear equations {a_1x+b_1y+c_1z=d_1; a_2x+b_2y+c_2z=d_2; a_3x+b_3y+c_3z=d_3, (1) consider the determinant D=|a_1 b_1 c_1; a_2 b_2 c_2; a_3 b_3 c_3|. (2) Now ...

A number which is simultaneously octagonal and pentagonal. Let O_n denote the nth octagonal number and P_m the mth pentagonal number, then a number which is both octagonal ...

A regular number, also called a finite decimal (Havil 2003, p. 25), is a positive number that has a finite decimal expansion. A number such as 1/3=0.33333... which is not ...

Watson (1939) considered the following three triple integrals, I_1 = 1/(pi^3)int_0^piint_0^piint_0^pi(dudvdw)/(1-cosucosvcosw) (1) = (4[K(1/2sqrt(2))]^2)/(pi^2) (2) = ...