How to make a double loop to evaluate this triple integral

[Safinazsalem]

I have a function f(t1,t2,t3, a,k) where I make a triple integral over t1,t2,t3 and make a loop on the value of the variable "k"

-The integration limits of t1 and t2 are from 0 to a

-The integration limits of t3 is from 0 to infinity

The question is how to make a second loop over the variable a where it tends to zero

Here is the code that I use:

# %%
import numpy as np
import scipy.special
from scipy import integrate
from scipy.special import kn
import matplotlib.pyplot as plt
import math
import time, sys


H=4.10061*10**-5;ti=-100*H;end=-H;step=H;a=0;

f = lambda t1, t2,t3, k: t1 + t2 +k +  a +t3
X = np.arange(0,50,0.1)

g=float('inf')
#plot(X,f(X))

def F(x):
    res = np.zeros_like(x)
    for i,val in enumerate(x):
        y,err = integrate.tplquad(f, 0, a,lambda x: 0, lambda x: a,lambda x,y: 0, lambda x,y: g,args=(val,))
        res[i]=y/(math.exp(H*a)**2)
    return res

plt.plot(X,F(X))
plt.title("P(k)")
plt.show()

As you glance that in this code I write f(t1,t2,t3,k) and let a=0. But that makes the integral vanishes

So how to adjust this code and write f(t1,t2,t3,a,k) then run a second loop on "a" as a variable like "k" such that "a" tends to zero.


Any help is appreciated!