The document discusses the use of the gamma function from the SciPy library and includes Python code for its implementation. It demonstrates computing the gamma function for various inputs, including complex numbers, and visualizes the results using Matplotlib. The plot compares the gamma function values with factorial values, intended for educational purposes.

1. In [11]: # Orignal-source/copyrights of:Sci Py website,https://docs.scipy.org/
# Demonstration of use of gamma function
from scipy.special import gamma, factorial #import function from library
In [12]: gamma([0, 0.5, 1, 5])#scipy.special.gamma(z, out=None) = <ufunc 'gamma'>
In [13]: z = 2.5 + 1j # Initialize a complex number
gamma(z) # Pass the complex number to gamma function
In [14]: import numpy as np #import numpy from libraries
x = np.linspace(-3.5, 5.5, 2251) #numpy.linspace(start, stop, num=50, end
point=True, retstep=False, dtype=None, axis=0)
y = gamma(x)
In [15]: import matplotlib.pyplot as plt #import pyplot from libraries
plt.plot(x, y, 'b', alpha=0.6, label='gamma(x)') #pass gamma as a input t
o the plot
k = np.arange(1, 7) # define range
plt.plot(k, factorial(k-1), 'k*', alpha=0.6,
label='(x-1)!, x = 1, 2, ...')
plt.xlim(-3.5, 5.5) # define plt x limit
plt.ylim(-10, 25) # define plt y limit
plt.grid()
plt.xlabel('x')
plt.legend(loc='lower right')
plt.show() # draw plot
In [16]: # Original link 2022: https://docs.scipy.org/doc/scipy/reference/generate
d/scipy.special.gamma.html#scipy.special.gamma
# Executed by Bhadale IT, in Anaconda Jupyter Notebook
# No copyright infringement intended, for educational purpose only
Out[12]: array([ inf, 1.77245385, 1. , 24. ])
Out[13]: (0.77476210455108419+0.70763120437959348j)
NIST_Fns http://localhost:8888/nbconvert/html/NIST_Fns.ipynb?download=false
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