Question

Gamma(2/3)*gamma(1/3)

Answer 1

Answer:

( Gama 2/3 ) ( Gama 1/3 )

Gama ( 2/3 x 1/3 )

Gama ( 2/9 )

Answer 2

Answer:

The value of F(1/3)F(1 - 1/3) by using Euler's reflection formula is 2π.

Step-by-step explanation:

A relationship between f(a - x) and f(x) is known as a reflection relation or reflection formula in mathematics. It is a particular instance of a functional equation, and the phrase "functional equation" is frequently used in the literature in place of "reflection formula."

For the numerical computation of specific functions, reflection formulas are helpful. In practise, all arguments can be represented by an approximation that is more accurate or only converges on one side of a reflection point (usually on the positive half of the complex plane).

Given, the equation is gamma(2/3)×Gamma(1/3)

According to the Euler's reflection formula.

F(x)F(1-x) = π/sinπx

So, F(1/3)F(1 - 1/3) = π/sin(π/3)

⇒ F(1/3)F(1 - 1/3) = π/(1/2)

⇒ F(1/3)F(1 - 1/3) = 2π

Hence, the value of F(1/3)F(1 - 1/3) by using Euler's reflection formula is 2π.

To know more about Euler's reflection formula, click on the link below:

https://brainly.in/question/6659824

To know more about functional equation, click on the link below:

https://brainly.in/question/1432775

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