File:Gamma plus sin pi z.png

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Gamma_plus_sin_pi_z.png ‎(630 × 470 pixels, file size: 41 KB, MIME type: image/png)

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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)
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Source Own work
Author Wolfmankurd

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Date/TimeThumbnailDimensionsUserComment
current11:07, 11 June 2018Thumbnail for version as of 11:07, 11 June 2018630 × 470 (41 KB)Wolfmankurd (talk | contribs)Added differential colouring, added grid lines, more detail and larger size
16:43, 10 June 2018Thumbnail for version as of 16:43, 10 June 2018370 × 238 (13 KB)Wolfmankurd (talk | contribs)User created page with UploadWizard

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