Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Gamma Function - Properties & Its Application
Gamma Function - Properties & Its Application Video Lecture | Mathematics for Competitive Exams
|
98 videos|27 docs|30 tests
|
FAQs on Gamma Function - Properties & Its Application Video Lecture - Mathematics for Competitive Exams
| 1. What is the gamma function and what are its properties? |  |
Ans. The gamma function, denoted by Γ(x), is an extension of the factorial function for non-integer values. It is defined as Γ(x) = ∫[0, ∞] t^(x-1) * e^(-t) dt. The properties of the gamma function include:
- Γ(x+1) = x * Γ(x), which is a recursive formula.
- Γ(1) = 1 and Γ(1/2) = √π, which are special values.
- Γ(n) = (n-1)! for positive integers n, which shows the relationship with the factorial function.
| 2. How is the gamma function used in mathematics? | |
Ans. The gamma function has various applications in mathematics. Some of them include:
- Evaluating definite integrals that involve exponential functions.
- Solving differential equations and boundary value problems.
- Approximating factorials and binomial coefficients for non-integer values.
- Calculating special functions such as the beta function and the incomplete gamma function.
| 3. Can the gamma function be evaluated for negative values? | |
Ans. Yes, the gamma function can be evaluated for negative values except for non-positive integers. For negative x, Γ(x) is related to Γ(x+1) through the formula Γ(x) = -x * Γ(x+1). This property allows the gamma function to be extended to the complex plane.
| 4. What is the relationship between the gamma function and the factorial function? | |
Ans. The gamma function is an extension of the factorial function. For positive integers n, Γ(n) = (n-1)!. This relationship allows us to calculate factorials for non-integer values using the gamma function.
| 5. Are there any practical applications of the gamma function outside of mathematics? | |
Ans. Yes, the gamma function finds applications in various fields beyond mathematics. Some examples include:
- Physics: The gamma function is used in quantum mechanics to determine probabilities of quantum states and calculate transition probabilities.
- Statistics: The gamma function is utilized in probability distributions such as the gamma distribution and the chi-squared distribution.
- Engineering: The gamma function is employed in signal processing, image reconstruction, and pattern recognition algorithms.
- Finance: The gamma function is used in option pricing models such as the Black-Scholes model in quantitative finance.
Related Exams
About this Video
|
4.68/5 Rating |
|
Dec 23, 2024 Last updated |
Video Description: Gamma Function - Properties & Its Application for Mathematics 2024 is part of Mathematics for Competitive Exams preparation.
The notes and questions for Gamma Function - Properties & Its Application have been prepared according to the Mathematics exam syllabus.
Information about Gamma Function - Properties & Its Application covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Gamma Function - Properties & Its Application.
Introduction of Gamma Function - Properties & Its Application in English is available as part of our Mathematics for Competitive Exams for Mathematics & Gamma Function - Properties & Its Application in
Hindi for Mathematics for Competitive Exams course. Download more important topics related with notes, lectures and mock test series for
Mathematics Exam by signing up for free.
Description
Video Lecture & Questions for Gamma Function - Properties & Its Application Video Lecture | Mathematics for Competitive Exams - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for Competitive Exams.
Information about Gamma Function - Properties & Its Application
Here you can find the meaning of Gamma Function - Properties & Its Application defined & explained in the simplest way possible.
Besides explaining types of Gamma Function - Properties & Its Application theory, EduRev gives you an ample number of questions to practice Gamma Function - Properties & Its Application tests,
examples and also practice Mathematics tests.
|
98 videos|27 docs|30 tests
|
|
Explore Courses for Mathematics exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
past year papers
,Free
,Exam
,MCQs
,practice quizzes
,Viva Questions
,Gamma Function - Properties & Its Application Video Lecture | Mathematics for Competitive Exams
,Summary
,Sample Paper
,Semester Notes
,mock tests for examination
,shortcuts and tricks
,Objective type Questions
,Gamma Function - Properties & Its Application Video Lecture | Mathematics for Competitive Exams
,Important questions
,Previous Year Questions with Solutions
,study material
,ppt
,video lectures
,Extra Questions
,Gamma Function - Properties & Its Application Video Lecture | Mathematics for Competitive Exams
;
Study Gamma Function - Properties & Its Application on the App
Students of Mathematics can study Gamma Function - Properties & Its Application alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Gamma Function - Properties & Its Application,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Gamma Function - Properties & Its Application is prepared as per the latest Mathematics syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup