Search Results for ""

The variable phi (also denoted am(u,k)) used in elliptic functions and elliptic integrals is called the amplitude (or Jacobi amplitude). It can be defined by phi = am(u,k) ...

The sequence of numbers {j_n} giving the number of digits in the three-fold power tower n^(n^n). The values of n^(n^n) for n=1, 2, ... are 1, 16, 7625597484987, ... (OEIS ...

An integer j(n) is called a jumping champion if j(n) is the most frequently occurring difference between consecutive primes <=n (Odlyzko et al. 1999). This term was coined by ...

The Kubo-Martin-Schwinger (KMS) condition is a kind of boundary-value condition which naturally emerges in quantum statistical mechanics and related areas. Given a quantum ...

d sum OEIS 0 23.10344 A082839 1 16.17696 A082830 2 19.25735 A082831 3 20.56987 A082832 4 21.32746 A082833 5 21.83460 A082834 6 22.20559 A082835 7 22.49347 A082836 8 22.72636 ...

A tree with its nodes labeled. The number of labeled trees on n nodes is n^(n-2), the first few values of which are 1, 1, 3, 16, 125, 1296, ... (OEIS A000272). Cayley (1889) ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

Let L_n be the n×n matrix whose (i,j)th entry is 1 if j divides i and 0 otherwise, let Phi_n be the n×n diagonal matrix diag(phi(1),phi(2),...,phi(n)), where phi(n) is the ...

The Lehmer cotangent expansion for which the convergence is slowest occurs when the inequality in the recurrence equation b_k>=b_(k-1)^2+b_(k-1)+1. (1) for ...

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...