sigmoid, a Python code which evaluates the sigmoid function s(x)=1/(1+exp(-x)) or a derivative of any order. The test code creates graphic images.
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sigmoid is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
humps, a Python code which evaluates the humps() function, its first and second derivatives, and its antiderivative. The functions are plotted.
polpak, a Python code which evaluates a variety of mathematical functions, polynomials, and sequences, including Bell, Benford, Bernoulli, Bernstein, Cardan, Catalan, Charlier, Chebyshev, Collatz, Delannoy, Euler, Fibonacci, Gegenbauer, Gudermannian, Harmonic, Hermite, Hofstadter, Hypergeometric 2F1, Jacobi, Krawtchouk, Laguerre, Lambert W, Legendre, Lerch, Meixner, Mertens, Moebius, Motzkin, Phi, Stirling Numbers, Tau, Tribonacci, Zernike.
runge, a Python 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]. Plots of these functions are made.
sinc, a Python 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 Python code which evaluates the Steinerberger function, a continuous function with discontinuous derivative, which is very hard to accurately plot, integrate, minimize, or interpolate. Plots are made of several of the functions.
