File:Gamma plus sin pi z.svg

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Original file ‎(SVG file, nominally 576 × 426 pixels, file size: 23 KB)

Captions

Captions

A visualization showing how the gamma function is non unique

Summary[edit]

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.
Date
Source Original png graphic was made by Wolfmankurd and can be found at File:Gamma_plus_sin_pi_z.png
Author Eitanlees
SVG development
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W3C grn 
The SVG code is valid.
Created with Matplotlib-logo 
This plot was created with Matplotlib.
Source code
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Python code

import numpy as np
import matplotlib.pyplot as plt
from scipy.special import gamma

lb_x, ub_x = (-4.9, 4.5)
lb_y, ub_y = (-1.2, 5.2)

x = np.linspace(-5, 5, int(1e5))
y = gamma(x)
y[y > 2*ub_y] = np.inf
y[y < lb_y] = -np.inf

g = np.sin(np.pi*x) + y

fig, ax = plt.subplots(figsize=(8,6))
ax.plot(x, y, color = '#2020CE')
ax.plot(x, g, color = '#10CD30')
ax.set(
    xlim=(lb_x, ub_x),
    ylim=(lb_y, ub_y)
)

ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.spines['bottom'].set_position(('data',0))
ax.yaxis.set_ticks_position('left')
ax.spines['left'].set_position(('data',0))

ax.grid(True, linestyle='dashed')
plt.show()

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
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 history

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Date/TimeThumbnailDimensionsUserComment
current19:39, 16 July 2019Thumbnail for version as of 19:39, 16 July 2019576 × 426 (23 KB)Eitanlees (talk | contribs)Remove borders
19:30, 16 July 2019Thumbnail for version as of 19:30, 16 July 2019720 × 540 (24 KB)Eitanlees (talk | contribs)User created page with UploadWizard

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