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Differential Equations

The constants C_n defined by C_n=[int_0^infty|d/(dt)((sint)/t)^n|dt]-1. (1) These constants can also be written as the sums C_n=2sum_(k=1)^infty(1+x_k^2)^(-n/2), (2) and ...

An invariant of an elliptic curve given in the form y^2=x^3+ax+b which is closely related to the elliptic discriminant and defined by j(E)=(2^83^3a^3)/(4a^3+27b^2). The ...

A sequence of real numbers {x_n} is equidistributed on an interval [a,b] if the probability of finding x_n in any subinterval is proportional to the subinterval length. The ...

The recursive sequence generated by the recurrence equation Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2)), with Q(1)=Q(2)=1. The first few values are 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, ... (OEIS ...

Landau's problems are the four "unattackable" problems mentioned by Landau in the 1912 Fifth Congress of Mathematicians in Cambridge, namely: 1. The Goldbach conjecture, 2. ...

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 ...

An ordered factorization is a factorization (not necessarily into prime factors) in which a×b is considered distinct from b×a. The following table lists the ordered ...

Sexy primes are pairs of primes of the form (p, p+6), so-named since "sex" is the Latin word for "six.". The first few sexy prime pairs are (5, 11), (7, 13), (11, 17), (13, ...

A sum-free set S is a set for which the intersection of S and the sumset S+S is empty. For example, the sum-free sets of {1,2,3} are emptyset, {1}, {2}, {3}, {1,3}, and ...