Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks

Exams
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology

EXAM TYPES

GCSE

IGCSE

AS

A Level

International A Level

University Admissions Tests

GCSE SUBJECTS

GCSE 1

GCSE 2

GCSE 3

GCSE 4

GCSE 5

SOME-TEXT

IGCSE SUBJECTS

IGCSE 1

AS SUBJECTS

AS 1

A Level SUBJECTS

A Level 1

International A Level SUBJECTS

International A Level 1

University Admissions Tests SUBJECTS

University Admissions Tests 1
Features
Features

Discover all of these amazing features with a free account.

Flashcards

Vaia AI

Notes

Study Plans

Study Sets
What’s new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
Resources
Discover

All the hacks around your studies and career - in one place.

Find a job

Find a degree

Student Deals

Magazine

Mobile App
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

Job Board
The largest student job board with the most exciting opportunities.

Vaia Deals
Verified student deals from top brands.

Our App
Discover our mobile app to take your studies anywhere.

Go to App

Learning Materials

Features

Discover

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

01

Given information

The given term to simplify is

02

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.

$Γ (p + 1) = p Γ (p)$

03

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 $\begin{array}{rcl} \frac{9}{10} \end{array}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The function $ψ (p) = \frac{d}{d p} I n Γ (p)$ is called the digamma function, and the polygama functions are defined by $ψ^{n} (p) = \frac{d^{n}}{d p^{n}} ψ (p)$ . [Warning: Some authors define $ψ (p)$ as $\frac{d}{d p} I n (p!) = \frac{d}{d p} I n Γ (p + 1)$ ).]

(a) Show that $ψ (p + 1) = ψ (p) + \frac{1}{p}$ . Hint: See (3.4).

(b) Use Problem 6 to obtain $ψ (p) □ I n (p) - \frac{1}{2 p} - \frac{1}{12 p^{2}} . . .$ .

Use a graph of $s i n^{2} θ$ and the text discussion just before (12.4)to verify the equations (12.4). Note that the area under the $s i n^{2} θ$ graph from $0 - \frac{π}{2}$ and the area from $\frac{π}{2} - π$ are mirror images of each other, and this will be true also for any function of $\sin^{2} θ$ .

Prove that

$\begin{matrix} \frac{d}{d p} Γ (p) = \int_{0}^{\infty} x^{p - 1} e^{- x} l n x d x \\ \frac{d^{n}}{d p^{n}} Γ (p) = \int_{0}^{\infty} x^{p - 1} e^{- x} {(l n x)}^{n} d x \end{matrix}$

Express the following integrals as $β$ functions, and then, by (7.1) , in terms of $Γ$ functions. When possible, use $Γ$ function formulas to write an exact answer in terms of $π, 2$ , etc. Compare your answers with computer results and reconcile any discrepancies.

role="math" localid="1664349717981" $\int_{0}^{1} \frac{x^{4}}{\sqrt{1 - x^{2}}} d x$

In Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.

7. $\int_{0}^{\frac{5 π}{4}} \sqrt{25 - s i n^{2} θ} d θ$

See all solutions

Recommended explanations on Physics Textbooks

Electricity

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Magnetism

Read Explanation

Waves Physics

Read Explanation

Famous Physicists

Read Explanation

Atoms and Radioactivity

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free