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

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Drawing 2024-4-9，9:15

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https://ww2.mathworks.cn/matlabcentral/answers/2104711-how-to-get-an-expression-for-a-hypergeometric-function-with-symbiotic-variable

评论： Drawing 2024-4-11，6:32

采纳的回答： Torsten

在 MATLAB Online 中打开

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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Answer 1

Torsten 2024-4-9，17:18

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https://ww2.mathworks.cn/matlabcentral/answers/2104711-how-to-get-an-expression-for-a-hypergeometric-function-with-symbiotic-variable#answer_1438831

移动：Torsten 2024-4-9，17:18

MATLAB is not able to find the Inverse Laplace transform of such a complicated function as an analytic expression.

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Torsten 2024-4-10，9:48

What kind of simplified representation of 125000.0*hypergeom([-0.90909, 4.0], 0.090909, -1.342e-9*s) - 125000.0 do you expect to get ? "hypergeom" is defined by an infinite series expression. Do you think this will be easier to handle for "ilaplace" ?

Drawing 2024-4-11，6:32

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.

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