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Let $z$ be a complex element in the unit disc. Let's consider an integral transform from $0$ to $\infty$ denoted by $R_{n,m}(f)(z)$ with two fixed parameters $n$ and $m$ where $f$ is a square integrable function on $\mathbb{R^+}$.

I wish to draw graph in $3D$ in general for $n=0,m=0$ and $n=1,m=0$ and $n=0,m=1$ and $n=1,m=1$ and $n=1,m=2$ and $n=2,m=1$ and $n=2,m=2$ and $n=2,m=3$ and $n=3,m=2$ and $n=3,m=3$.

For example

  • Image for Bessel functions
    enter image description here

  • Image Generalized Laguerre polynomials
    enter image description here

Same problem for infinite series, I have tried the following program just for $m=1$ and $n=1$ but it showed an error.

import matplotlib.pyplot as plt
import sympy as sym
import math
import numpy as np

from mpl_toolkits.mplot3d import Axes3D

x=np.linespace(0.0,0.5,20)
y=np.linespace(0.0,0.5,20)

n=1
m=1
z=complex(x,y)

def zero_to_infinity():
    i = 0

    while True:
        yield i
        i += 1

def CalcMYSeries(x,y):
    res, temp = 0, 0
    for i in zero_to_infinity():
        res += ((math.gamma(i+n+m))*((z)**i) )
        if res == temp:
            break
        temp = res
    return res

f=CalcMYSeries(x,y)

X, Y= np.meshgrid(x, y)

F=f(X,Y)

fig=plt.figure(figsize=[12,8])
ax = fig.gca(projection = '3d')
ax.plot_surface(X, Y, F, cmap=cm.coolwarm)

plt.show()

I have tried this many times but it didn't work. How to plot this series $K_{n,m}(z)$ for $z$ in the complex unit disc? Moreover, how to write modified Bessel function in python?

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