page_title: Beta function
hierarchical_section_title: Beta function
caption_attribution_description: English: A contour plot of the beta function. Created using the following Sage code: from math import isnan from scipy import stats def beta2(x, y): return (gamma(x) * gamma(y)) / gamma(x + y) vals = [beta2(a, b) for a in srange(-2, 2, 0.2) for b in srange(-2, 2, 0.2)] # test values to work out contours filtered = filter(lambda num: (not isnan(num)) and (-1000 &lt; num &lt; 1000), vals) contours = stats.mstats.mquantiles(filtered, srange(0, 1, 1/15)) contour_plot(beta2, (x, -3, 3), (y, -3, 3), cmap=&#39;rainbow&#39;, contours=contours)
context_page_description: In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral
  for complex number inputs x, y such that Re x > 0, Re y > 0.
  The beta function was studied by Euler and Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital beta.
context_section_description: In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients.  It is defined by the integral
  for complex number inputs x, y such that Re x > 0, Re y > 0.
  The beta function was studied by Euler and Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital beta.
caption: Contour plot of the beta function
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