File:Gamma plus sin pi z.svg
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.Category:Valid SVG created with Matplotlib code#Gamma%20plus%20sin%20pi%20z.svg |
| 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()
|
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