Aula 03 | Métodos Aplicados de Matemática II - Um exemplo de Funções especiais - Bessel

Описание: Como obter a função de Bessel via método de Frobenius

Códigos:
--- Bessel -------------------------------
import numpy as np
import scipy.special as sp
import matplotlib.pyplot as plt

plt.matplotlib.rc('text', usetex = True)
plt.matplotlib.rc('grid', linestyle = 'dotted')
plt.matplotlib.rc('figure', figsize = (6.4,4.8)) # (largura,altura) polegadas
x = np.linspace(0, 15, 500)
for v in range(0, 6):
plt.plot(x, sp.jv(v, x))

plt.xlim((0, 15))
plt.ylim((-0.5, 1.1))
plt.legend(('${J}_0(x)$', '${J}_1(x)$', '${J}_2(x)$','${J}_3(x)$', '${J}_4(x)$', '${J}_5(x)$'), loc = 0)
plt.xlabel('$x$')
plt.ylabel('${J}_n(x)$')
plt.grid(True)
plt.tight_layout(0.5)
plt.savefig('example-04-fig.pdf')
np.savetxt('example-04.txt',list(zip(x,sp.jv(0,x),sp.jv(1,x),sp.jv(2,x),sp.jv(3,x),sp.jv(4,x),sp.jv(5,x))),
fmt="% .10e")
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---Gamma ------------------------------
from scipy.special import gamma, factorial
import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-3.5, 5.5, 2251)
y = gamma(x)

plt.plot(x, y, color='blue')
plt.xlim(-3.5, 5.5)
plt.ylim(-10, 25)
plt.savefig('gamma.png')
plt.xlabel('x')
plt.show()
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