\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) \( \newcommand{\cm}{\mathrm{cm} } \) \( \newcommand{\sec}{ \, \mathrm{sec} \, } \) \( \newcommand{\units}[1]{\,\text{#1}} \) \( \newcommand{\vhat}[1]{\,\hat{#1}} \) \( \newcommand{\vhati}{\,\hat{i}} \) \( \newcommand{\vhatj}{\,\hat{j}} \) \( \newcommand{\vhatk}{\,\hat{k}} \) \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) \( \newcommand{\norm}[1]{\|{#1}\|} \) \( \newcommand{\arccot}{ \, \mathrm{arccot} \, } \) \( \newcommand{\arcsec}{ \, \mathrm{arcsec} \, } \) \( \newcommand{\arccsc}{ \, \mathrm{arccsc} \, } \) \( \newcommand{\sech}{ \, \mathrm{sech} \, } \) \( \newcommand{\csch}{ \, \mathrm{csch} \, } \) \( \newcommand{\arcsinh}{ \, \mathrm{arcsinh} \, } \) \( \newcommand{\arccosh}{ \, \mathrm{arccosh} \, } \) \( \newcommand{\arctanh}{ \, \mathrm{arctanh} \, } \) \( \newcommand{\arccoth}{ \, \mathrm{arccoth} \, } \) \( \newcommand{\arcsech}{ \, \mathrm{arcsech} \, } \) \( \newcommand{\arccsch}{ \, \mathrm{arccsch} \, } \)

17Calculus - Gamma Function

17Calculus
Single Variable Calculus
Derivatives
Integrals
Multi-Variable Calculus
Precalculus
Functions

Gamma Function

Resources

Topics You Need To Understand For This Page

improper integrals

Related Topics and Links

Wikipedia - Gamma Function

SOS Math - Gamma Function

Equations

\[ \Gamma(t) = \int_0^{\infty}{ x^{t-1}e^{-x}~dx } \]

The gamma function is related to factorials by the fact that for positive integers, the property \( \Gamma(n) = (n-1)! \) holds.
Here is a video clip discussing the properties of the gamma function.   This clip is within the context of Laplace Transforms but you do not need to understand Laplace Transforms in order to understand what he is talking about.

Trefor Bazett - Properties of the Gamma Function

video by Trefor Bazett

Applications

We can use the gamma function to find this Laplace Transform.

Calculate \( \mathcal{L}\{ t^n \} \) using the gamma function.

Problem Statement

Calculate \( \mathcal{L}\{ t^n \} \) using the gamma function.

Final Answer

\( \mathcal{L}\{ t^n \} \) \( = \dfrac{n!}{s^{n+1}} \)

Problem Statement

Calculate \( \mathcal{L}\{ t^n \} \) using the gamma function.

Solution

Trefor Bazett - 4377 video solution

video by Trefor Bazett

Final Answer

\( \mathcal{L}\{ t^n \} \) \( = \dfrac{n!}{s^{n+1}} \)

Log in to rate this practice problem and to see it's current rating.

Really UNDERSTAND Calculus

Log in to rate this page and to see it's current rating.

To bookmark this page and practice problems, log in to your account or set up a free account.

Search Practice Problems

Do you have a practice problem number but do not know on which page it is found? If so, enter the number below and click 'page' to go to the page on which it is found or click 'practice' to be taken to the practice problem.

memorize to learn

Try Audible Premium Plus and Get Up to Two Free Audiobooks

As an Amazon Associate I earn from qualifying purchases.

I recently started a Patreon account to help defray the expenses associated with this site. To keep this site free, please consider supporting me.

Support 17Calculus on Patreon

Practice Search

Do NOT follow this link or you will be banned from the site!

When using the material on this site, check with your instructor to see what they require. Their requirements come first, so make sure your notation and work follow their specifications.

DISCLAIMER - 17Calculus owners and contributors are not responsible for how the material, videos, practice problems, exams, links or anything on this site are used or how they affect the grades or projects of any individual or organization. We have worked, to the best of our ability, to ensure accurate and correct information on each page and solutions to practice problems and exams. However, we do not guarantee 100% accuracy. It is each individual's responsibility to verify correctness and to determine what different instructors and organizations expect. How each person chooses to use the material on this site is up to that person as well as the responsibility for how it impacts grades, projects and understanding of calculus, math or any other subject. In short, use this site wisely by questioning and verifying everything. If you see something that is incorrect, contact us right away so that we can correct it.

Links and banners on this page are affiliate links. We carefully choose only the affiliates that we think will help you learn. Clicking on them and making purchases help you support 17Calculus at no extra charge to you. However, only you can decide what will actually help you learn. So think carefully about what you need and purchase only what you think will help you.

We use cookies on this site to enhance your learning experience.

17calculus

Copyright © 2010-2022 17Calculus, All Rights Reserved     [Privacy Policy]     [Support]     [About]

mathjax.org
Real Time Web Analytics