File:Gamma plus sin pi z.png
Gamma_plus_sin_pi_z.png (630 × 470 pixels, file size: 41 KB, MIME type: image/png)
Captions
Summary
[edit]DescriptionGamma plus sin pi z.png |
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 |
Licensing
[edit]- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File:Gamma plus sin pi z.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
File:Gamma plus sin pi z.png → File:Gamma plus sin pi z.svg
For more information, see Help:SVG.
|
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 11:07, 11 June 2018 | 630 × 470 (41 KB) | Wolfmankurd (talk | contribs) | Added differential colouring, added grid lines, more detail and larger size | |
16:43, 10 June 2018 | 370 × 238 (13 KB) | Wolfmankurd (talk | contribs) | User created page with UploadWizard |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on vi.wikipedia.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Horizontal resolution | 39.37 dpc |
---|---|
Vertical resolution | 39.37 dpc |