File:Gamma plus sin pi z.png
Summary
| Description |
English: The Gamma function analytically continues the factorial function to non-integers. However it is not unique in this.
Here a periodic function which is 0 at the integer values shows how it may be added to the gamma function resulting in another analytic continuation of the factorials. Generated with sympy with jupyter. g = \\int_{0}^{\\infty} x^{z - 1} e^{- x}\\, dx h = \\sin{\\left (\\pi z \\right )} + \\int_{0}^{\\infty} x^{z - 1} e^{- x}\\, dx plot(h, g, (z, 1, 4), axis_center=(1,1), ylabel="", xlabel="") Sage version plotted with plot([gamma(x), gamma(x)+sin(pi*x)], x,-5, 5, ymax=5, ymin = -1, detect_poles=True, gridlines=True, ticks_integer=True) |
| Date | |
| Source | Own work |
| Author | Wolfmankurd |
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