How to get an expression for a Hypergeometric function with symbiotic variable

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Drawing
Drawing 2024-4-9
编辑： Muhammad Abdullah 2024-7-15
I want to calculate the inverse Laplace transform of ,
where G(r)= , s is the variable.
My code can't compute a Hypergeometric function function with symbolic variable, and it can't get a concrete inverse Laplace transformation.
here is my code
phi=4;alpha=2.2;beta=4.7e-05;rho=25;r1=500;r2=400;lambda=4.0e-05;
syms s r t
G_r=0.5*r^2*(hypergeom([phi,-2/alpha],(alpha-2)/alpha,-r^(-alpha)*beta*rho*s )-1);
L_IBd00_s=exp(2*pi*lambda*( vpa(subs(G_r,r,r1),5) -vpa(subs(G_r,r,r2),5) ));
L_IBd00_inv=ilaplace(1/s*L_IBd00_s);
the result is
>> vpa(subs(G_r,r,radius),5)
ans =
125000.0*hypergeom([-0.90909, 4.0], 0.090909, -1.342e-9*s) - 125000.0
>> vpa(L_IBd00_inv,5)
ans =
0.000012253*heaviside(t)*ilaplace(exp(10.0*pi*hypergeom([-0.90909, 4.0], 0.090909, -1.342e-9*s) - 6.4*pi*hypergeom([-0.90909, 4.0], 0.090909, -2.1926e-9*s))/s, s, t)
So how can i get an expression of L_IBd00_inv with respect to the variable t?

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采纳的回答

Torsten
Torsten 2024-4-9
移动：Torsten 2024-4-9
MATLAB is not able to find the Inverse Laplace transform of such a complicated function as an analytic expression.
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Drawing
Drawing 2024-4-11
Hello, Torsten! I thought i can get a simplified representation like " hypergeom([4.2,-1],2.2,1.1*s ) ans =1 - (21*s)/10", so that this will be easier to handle for "ilaplace" .
I read this opinion from a paper, the author mentioned "the inverse Laplace transform of 1/s*" can be computed directly in MATLAB.
Muhammad Abdullah
Muhammad Abdullah 2024-7-15
编辑：Muhammad Abdullah 2024-7-15
@Drawing Did you solve the problem, i have a similar problem related to hypergeom function (1F1) and then computing its inverse transform.
Following is the expression
z = 10.43*s/(s+1.0)
this will be passed to 1F1 and the result is
hypergeom(1.3, 14.3, -(10.43*s)/(s + 1.0))
need to evaluate this equation and then have to compute its inverse laplace transform...

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更多回答（1 个）

Muhammad Abdullah
hello, I want to calculate the inverse laplace transform of a characteristic function
this is the fourier transform of h(x), which is converted to Laplace transform with p = -i*t
from here we make a characteristic function which is
this characteristic function is converted to hypergeometric function
I have to get the inverse laplace transform of this function, I have written the following code:
N = 3; x_bar = 2.5; a = 1.3; b = 13; c = a+b;
syms s t
p = -1*1j*s
z = -1*((N*x_bar*(c/a)*p)/(p+1))
h = hypergeom(a,c,z)
C_slow = h/((p+1)^N)
f(t) = ilaplace(C_slow)
output of code:
z =
-(s*165i)/(2*(- 1 + s*1i))
h =
hypergeom(13/10, 143/10, -(s*165i)/(2*(- 1 + s*1i)))
do we have to put the vlaue of ''s'' to evalute the hypergeom function? I don't know what i am missing here...any help would be appreciated

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