File:Partial sums riemann zeta function.svg
Summary
| Description |
English: The 30 first partial sums of Riemann's zeta function, for s = 1 and 2 (real numbers). This corresponds to the harmonic series, and the series introduced in the Basel problem. |
| Date | |
| Source | Own work |
| Author | Åshild Telle |
| Other versions | File:Partial sums riemann zeta function-no.svg, File:Partial sums riemann zeta function.png, File:Partial sums riemann zeta function-no.png |
| SVG development | |
| Source code | Python codeimport numpy as np
import matplotlib.pyplot as plt
def riemann_zeta_fn(n : int, s : complex) -> np.ndarray:
"""
Args_
n - number of points to plot
s - exponential
Returns:
numpy array of length n; values for the first n
terms in the series defining the riemann zeta function
"""
n_values = np.arange(1, n+1)
sequence_values = np.array([1/(n**s) for n in n_values])
return n_values, np.cumsum(sequence_values)
n = 30
n_values, riemann1 = riemann_zeta_fn(n, 1)
n_values, riemann2 = riemann_zeta_fn(n, 2)
label1 = r"$\sum_{n = 1}^{\infty} \frac{1}{n}$"
label2 = r"$\sum_{n = 1}^{\infty} \frac{1}{n^2}$"
plt.plot(n_values, riemann1, '*', label=label1)
plt.plot(n_values, riemann2, 'xb', label=label2)
plt.xlabel("n")
plt.ylabel("Partial sums")
plt.legend(fontsize=15)
plt.savefig("riemann_zeta_s1and2.svg")
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Licensing
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