Chapter 11: Q3P (page 540)

Use the recursion relation (3.4), and if needed, equation (3.2) to simplify:
$Γ (\frac{2}{3}) / Γ (\frac{8}{3})$

Short Answer

Expert verified

The value of $Γ (\frac{2}{3}) / Γ (\frac{8}{3})$ is $\frac{9}{10}$

Step by step solution

Given information

The given term to simplify is

Concept and formula

A recurrence relation in mathematics is an equation that represents the nth term of a series as a function of the k preceding terms, for some fixed k known as the order of the relation.

The formula to be used is given below.

$Γ (p + 1) = p Γ (p)$

Apply the formula

Solve the expression

$\begin{array}{rcl} Γ (\frac{8}{3}) & = & Γ (\frac{5}{3} + 1) \\ Γ (\frac{8}{3}) & = & \frac{5}{3} Γ (\frac{5}{3}) \\ Γ (\frac{8}{3}) & = & \frac{5}{3} (\frac{2}{3}) Γ (\frac{2}{3}) \\ Γ (\frac{2}{3}) / Γ (\frac{8}{3}) & = & \frac{9}{10} \end{array}$

The value of given term is $\begin{array}{rcl} \frac{9}{10} \end{array}$

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Use the recursion relation (3.4), and if needed, equation (3.2) to simplify:
$Γ (\frac{2}{3}) / Γ (\frac{8}{3})$

Short Answer

Step by step solution

Given information

Concept and formula

Apply the formula

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Use the recursion relation (3.4), and if needed, equation (3.2) to simplify:Γ(23)/Γ(83)

Short Answer

Step by step solution

Given information

Concept and formula

Apply the formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

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Linear Momentum

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Study anywhere. Anytime. Across all devices.

Use the recursion relation (3.4), and if needed, equation (3.2) to simplify:
$Γ (\frac{2}{3}) / Γ (\frac{8}{3})$