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The method for solving the Goursat problem and Cauchy problem for linear hyperbolic partial differential equations using a Riemann function.

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z], is said to be k-balanced if sum_(i=1)^qbeta_i=k+sum_(i=1)^palpha_i.

A real-valued univariate function f=f(x) is said to have a removable discontinuity at a point x_0 in its domain provided that both f(x_0) and lim_(x->x_0)f(x)=L<infty (1) ...

The so-called explicit formula psi(x)=x-sum_(rho)(x^rho)/rho-ln(2pi)-1/2ln(1-x^(-2)) gives an explicit relation between prime numbers and Riemann zeta function zeros for x>1 ...

The inverse erf function is the inverse function erf^(-1)(z) of the erf function erf(x) such that erf(erf^(-1)(x)) = x (1) erf^(-1)(erf(x)) = x, (2) with the first identity ...

A three-dimensional data set consisting of stacked two-dimensional data slices as a function of a third coordinate.

Let f(z) be an analytic function in |z-a|<R. Then f(z)=1/(2pi)int_0^(2pi)f(z+re^(itheta))dtheta for 0<r<R.

A point x_0 is said to be a periodic point of a function f of period n if f^n(x_0)=x_0, where f^0(x)=x and f^n(x) is defined recursively by f^n(x)=f(f^(n-1)(x)).

5((x^5)_infty^5)/((x)_infty^6)=sum_(m=0)^inftyP(5m+4)x^m, where (x)_infty is a q-Pochhammer symbol and P(n) is the partition function P.

Let f be a bounded analytic function on D(0,1) vanishing to order m>=0 at 0 and let {a_j} be its other zeros, listed with multiplicities. Then ...