File:Gamma plus sin pi z.svg
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 576 × 426 pixels. Other resolutions: 320 × 237 pixels | 640 × 473 pixels | 1,024 × 757 pixels | 1,280 × 947 pixels | 2,560 × 1,893 pixels.
Original file (SVG file, nominally 576 × 426 pixels, file size: 23 KB)
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. |
| 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 |  This plot was created with Matplotlib. |
| Source code | Python codeimport 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
I, the copyright holder of this work, hereby publish it under the following license:
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
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:39, 16 July 2019 | | 576 × 426 (23 KB) | wikimediacommons>Eitanlees | Remove borders |
File usage
The following page uses this file:
