fresnel, a C++ code which evaluates the Fresnel cosine and sine integrals.
The Fresnel integrals are defined as:
c(x) = Integral ( 0 <= t <= x ) cos(pi/2 t^2) dt
s(x) = Integral ( 0 <= t <= x ) sin(pi/2 t^2) dt
(Some definitions omit the factor of pi/2.)
The information on this web page is distributed under the MIT license.
fresnel is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
dirichlet, a C++ code which evaluates the Dirichlet kernel function, sometimes called the periodic sinc function. The function includes a parameter n, normally taken to be an integer. The function is defined by diric(x,n)=sin(0.5*n*x)/n/sin(0.5*x). Sample plots of these functions are made.
gaussian, a C++ code which evaluates the Gaussian function for arbitrary mu and sigma, its antiderivative, and derivatives of arbitrary order.
humps, a C++ code which evaluates the humps() function, its first and second derivatives, and its antiderivative. The functions are plotted.
runge, a C++ code which evaluates the Runge() function, its first and second derivatives, and its antiderivative. This function causes a breakdown for polynomial interpolation over equally spaced nodes in [-1,+1]. The functions are plotted.
sigmoid, a C++ code which evaluates the sigmoid function s(x)=1/(1+exp(-x)) or its derivatives of any order. The test code creates graphic images.
sinc, a C++ code which evaluates the sinc() function, its first and second derivative and its antiderivative. The normalized function is defined by sincn=sin(pi*x)/(pi*x), the unnormalized function is sincu=sin(x)/x. Plots of these functions are made.
steinerberger, a C++ code which evaluates the Steinerberger function, a continuous function with discontinuous derivative, which is very hard to accurately plot, integrate, minimize, or interpolate.