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The natural logarithm of 2 is a transcendental quantity that arises often in decay problems, especially when half-lives are being converted to decay constants. ln2 has ...

The conjecture that the number of alternating sign matrices "bordered" by +1s A_n is explicitly given by the formula A_n=product_(j=0)^(n-1)((3j+1)!)/((n+j)!). This ...

There are two definitions of the Carmichael function. One is the reduced totient function (also called the least universal exponent function), defined as the smallest integer ...

The Fibonacci number F_(n+1) gives the number of ways for 2×1 dominoes to cover a 2×n checkerboard, as illustrated in the diagrams above (Dickau). The numbers of domino ...

The squared norm of a four-vector a=(a_0,a_1,a_2,a_3)=a_0+a is given by the dot product a^2=a_mua^mu=(a^0)^2-a·a, (1) where a·a is the usual vector dot product in Euclidean ...

The Laplace-Carson transform F of a real-valued function f is an integral transform defined by the formula F(p)=pint_0^inftye^(-pt)f(t)dt. (1) In most cases, the function F ...

The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits are functions of the differential variable, (1) It is sometimes known as ...

A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely ...

Also called Radau quadrature (Chandrasekhar 1960). A Gaussian quadrature with weighting function W(x)=1 in which the endpoints of the interval [-1,1] are included in a total ...

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 ...