Integral after alpha parametrization

In summary, Integral after alpha parametrization is a mathematical technique that simplifies integrals by introducing a parameter, alpha, and manipulating it. It differs from traditional integration methods and has benefits such as simplifying difficult integrals and revealing patterns. It can be used for any type of integral, but its effectiveness may vary. However, it may not work for highly complex integrals and requires a certain level of mathematical knowledge and skill.
  • #1
jd24680
1
0
I have been stuck on the following double integral for some time:

∫(0 to inf) dα1 ∫(0 to inf) dα2 a1^(n1) * exp(-i (α1+α2) m^2) * (α1+α2)^(n2)

which arose after using alpha paremetrization on a Feynman integral. I was advised by my supervisor to use the substitution α1 = 1/2 (t+u) and α2 = 1/2 (t-u) but after doing this I fail to see how it helps.

Any advice on how to do this?

Thanks.
 
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  • #2
Show your work using the recommended substitutions. Perhaps you made an error in your algebra.
 

Related to Integral after alpha parametrization

1. What is "Integral after alpha parametrization"?

Integral after alpha parametrization is a mathematical technique used to simplify integrals by expressing them in terms of a parameter, alpha. This allows for easier evaluation and manipulation of the integral.

2. How is "Integral after alpha parametrization" different from traditional integration methods?

Unlike traditional integration methods, integral after alpha parametrization involves introducing a parameter, alpha, into the integral and then manipulating it to simplify the integral. This can make complex integrals easier to solve.

3. What are the benefits of using "Integral after alpha parametrization"?

One of the main benefits of using integral after alpha parametrization is that it can simplify integrals that would otherwise be difficult or impossible to solve. It can also help to reveal patterns and relationships between different integrals.

4. Can "Integral after alpha parametrization" be used for any type of integral?

Yes, integral after alpha parametrization can be used for any type of integral, including definite and indefinite integrals. However, the effectiveness of this method may vary depending on the complexity of the integral.

5. Are there any limitations or drawbacks to using "Integral after alpha parametrization"?

One limitation of integral after alpha parametrization is that it may not always work for highly complex integrals. In addition, it may require a certain level of mathematical knowledge and skill to effectively use this technique.

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