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Question: bug report: Wrong inverse Laplace transform. Maple 2024.2

Question:bug report: Wrong inverse Laplace transform. Maple 2024.2

nm 10401 Maple 2024
inttrans invlaplace
December 07 2024
4

Maple 2024.2 gives wrong inverse Laplace transform on expressions with exp(s) multiplied by Ei (the exponentional integral) with complex argument.

Below are two examples found so far. 

Inverse laplace of  exp(s)/2*Ei(1, s + I) gives exp(-I*(t + 1))/(2*(t + 2))  but the correct inverse should be exp(-I*(t + 1))/(2*(t + 1))

Inverse laplace of  exp(s)/2*Ei(1, s - I) gives exp(I*(t + 1))/(2*(t + 2))  but the correct inverse should be exp(I*(t + 1))/(2*(t + 1))

i.e. in both cases it gives 2*(t + 2) in denominator when denominator should be 2*(t + 1)

Below is worksheet

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1836 and is the same as the version installed in this computer, created 2024, December 2, 10:11 hours Pacific Time.`

> 

 

Example 1

 
> 

restart;

> 

Y:=exp(s)/2*Ei(1, s + I);
y_wrong:=inttrans:-invlaplace(Y,s,t)

(1/2)*exp(s)*Ei(1, s+I)

(1/2)*exp(-I*(t+1))/(t+2)

> 

#to show it is wrong, lets ask for the laplace transform of it. We see it is not the same as Y

> 

Y_back:=inttrans:-laplace(y_wrong,t,s): simplify(%);

(1/2)*exp(I+2*s)*Ei(1, 2*s+2*I)

> 

simplify(Y-Y_back);

(1/2)*exp(s)*Ei(1, s+I)-(1/2)*exp(I+2*s)*Ei(1, 2*s+2*I)

> 

#correct invlaplace should be exp(-I*(t + 1))/(2*(t + 1)). Proof:
y_correct:=exp(-I*(t + 1))/(2*(t + 1));

exp(-I*(t+1))/(2*t+2)

> 

Y_back:=inttrans:-laplace(y_correct,t,s);

(1/2)*exp(s)*Ei(1, s+I)

> 

simplify(Y-Y_back);

0

Example 2

 
> 

restart;

> 

Y:=exp(s)/2*Ei(1, s - I);
y_wrong:=inttrans:-invlaplace(Y,s,t)

(1/2)*exp(s)*Ei(1, s-I)

(1/2)*exp(I*(t+1))/(t+2)

> 

#to show it is wrong, let ask for the laplace transform of it. We see it is not the same as Y

> 

Y_back:=inttrans:-laplace(y_wrong,t,s): simplify(%);

(1/2)*exp(-I+2*s)*Ei(1, 2*s-2*I)

> 

simplify(Y-Y_back);

(1/2)*exp(s)*Ei(1, s-I)-(1/2)*exp(-I+2*s)*Ei(1, 2*s-2*I)

> 

#correct invlaplace should be exp(I*(t + 1))/(2*(t + 1)). Proof:
y_correct:=exp(I*(t + 1))/(2*(t + 1));

exp(I*(t+1))/(2*t+2)

> 

Y_back:=inttrans:-laplace(y_correct,t,s);

(1/2)*exp(s)*Ei(1, s-I)

> 

simplify(Y-Y_back);

0

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Download bug_in_inverse_laplace_transform.mw

 

Also Reported to Maple support.
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