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A class of formal series expansions in derivatives of a distribution Psi(t) which may (but need not) be the normal distribution function Phi(t)=1/(sqrt(2pi))e^(-t^2/2) (1) ...

Every nonconstant entire function attains every complex value with at most one exception (Henrici 1988, p. 216; Apostol 1997). Furthermore, every analytic function assumes ...

Krall and Fink (1949) defined the Bessel polynomials as the function y_n(x) = sum_(k=0)^(n)((n+k)!)/((n-k)!k!)(x/2)^k (1) = sqrt(2/(pix))e^(1/x)K_(-n-1/2)(1/x), (2) where ...

A method for computing the prime counting function. Define the function T_k(x,a)=(-1)^(beta_0+beta_1+...+beta_(a-1))|_x/(p_1^(beta_0)p_2^(beta_1)...p_a^(beta_(a-1)))_|, (1) ...

pi has decimal expansion given by pi=3.141592653589793238462643383279502884197... (1) (OEIS A000796). The following table summarizes some record computations of the digits of ...

The G-transform of a function f(x) is defined by the integral (Gf)(x)=(G_(pq)^(mn)|(a_p); (b_q)|f(t))(x) (1) =1/(2pii)int_sigmaGamma[(b_m)+s, 1-(a_n)-s; (a_p^(n+1))+s, ...

In the theory of special functions, a class of functions is said to be "of the third kind" if it is similar to but distinct from previously defined functions already defined ...

Erfc is the complementary error function, commonly denoted erfc(z), is an entire function defined by erfc(z) = 1-erf(z) (1) = 2/(sqrt(pi))int_z^inftye^(-t^2)dt. (2) It is ...

An Egyptian fraction is a sum of positive (usually) distinct unit fractions. The famous Rhind papyrus, dated to around 1650 BC contains a table of representations of 2/n as ...

The continued fraction for K is [2; 1, 2, 5, 1, 1, 2, 1, 1, ...] (OEIS A002211). A plot of the first 256 terms of the continued fraction represented as a sequence of binary ...