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J_m(x)=(2x^(m-n))/(2^(m-n)Gamma(m-n))int_0^1J_n(xt)t^(n+1)(1-t^2)^(m-n-1)dt, where J_m(x) is a Bessel function of the first kind and Gamma(x) is the gamma function.

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 length of a number n in base b is the number of digits in the base-b numeral for n, given by the formula L(n,b)=|_log_b(n)_|+1, where |_x_| is the floor function. The ...

For R[mu+nu]>0, |argp|<pi/4, and a>0, where J_nu(z) is a Bessel function of the first kind, Gamma(z) is the gamma function, and _1F_1(a;b;z) is a confluent hypergeometric ...

The central beta function is defined by beta(p)=B(p,p), (1) where B(p,q) is the beta function. It satisfies the identities beta(p) = 2^(1-2p)B(p,1/2) (2) = ...

where _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function and Gamma(z) is the gamma function (Bailey 1935, p. 16; Koepf 1998, p. 32).

An anti-analytic function is a function f satisfying the condition (df)/(dz)=0. (1) Using the result ...

A zero function is a function that is almost everywhere zero. The function sometimes known as "the zero function" is the constant function with constant c=0, i.e., f(x)=0 ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

For a discrete function f(n), the summatory function is defined by F(n)=sum_(k in D)^nf(k), where D is the domain of the function.