# Evaluating an integral issue

• I
• EngWiPy
In summary, the conversation discusses an integral that needs to be evaluated, but upon evaluating it, the result is infinite. The table of integrals provides a similar formula with certain conditions that must be met, and the person believes they have met all the conditions. However, there seems to be a problem with the argument for Ei, as it differs from the formula provided. The conversation ends with a request for more details on how the result of infinity was obtained.

#### EngWiPy

Hi,

I have the following integral that I want to evaluate:

$$\int_0^{\infty}y\,e^{-y\left[(z+1)(K-1)+1\right]}Ei\left(y_2(K-1)\right)\,dy$$

In the table of integrals there is a similar integral in the form

$$\int_0^{\infty}x^{v-1}\,e^{-\mu x}Ei\left(-\beta\,x\right)\,dx=-\frac{\Gamma(v)}{v(\mu+\beta)^v} 2F_1(1,\,v;\,v+1;\,\frac{\mu}{\mu+\beta})$$

and the conditions are ##|\arg{\beta}|<\pi##, ##Re\left\{\mu+\beta\right\}>0##, and ##Re\{v\}>0##. I think I meet all the conditions in my integral, but upon evaluating the result for ##z=2## and ##K=4##, it gives me ##\infty##!. Why?

There may be a problem with the argument for Ei. You have y2(K-1) (y2?) while the formula has ##-\beta x##.. Yours seem to be positive.

mathman said:
There may be a problem with the argument for Ei. You have y2(K-1) (y2?) while the formula has ##-\beta x##.. Yours seem to be positive.

Oh, it is ##y## not ##y_2##. You are right, the argument of Ei(.) in my case is positive, but there is no condition that says that ##\beta## has to be positive. It says that ##\Re\{\mu+\beta\}## is positive, which is met.

I haven't work with the ##F_1## function, but looking at the expression, how did you get ##\infty##? The denominator = 98.

mathman said:
I haven't work with the ##F_1## function, but looking at the expression, how did you get ##\infty##? The denominator = 98.

I think the absolute value of the last argument of 2F1 function must be less than one. In my case, the last argument is greater than one! But again, I am meeting the conditions of the integral, so, I why I get arguments that aren't right!

Give details!

## What is an integral issue?

An integral issue is a problem or topic that requires a comprehensive and thorough evaluation. It often involves multiple factors and perspectives, and its resolution can significantly impact individuals or society as a whole.

## Why is it important to evaluate an integral issue?

Evaluating an integral issue allows for a deeper understanding of its complexities and potential consequences. It also helps identify the most effective solutions and strategies for addressing the issue.

## What factors should be considered when evaluating an integral issue?

There are various factors to consider, including the root cause of the issue, its historical and cultural context, the stakeholders involved, and the potential short-term and long-term effects of different solutions.

## What methods can be used to evaluate an integral issue?

Some common methods for evaluating an integral issue include data analysis, surveys and interviews, case studies, and cost-benefit analysis. It is also important to consider diverse perspectives and involve experts in the field.

## How can the results of an integral issue evaluation be used?

The results of an integral issue evaluation can inform decision-making and policy development. They can also be used to raise awareness and initiate action towards addressing the issue. Further research and evaluation may also be necessary to continuously monitor and improve the situation.