Combinatorics | Unary operations | Gamma and related functions | Factorial and binomial topics
In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example,The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book Sefer Yetzirah. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of distinct objects: there are . In mathematical analysis, factorials are used in power series for the exponential function and other functions, and they also have applications in algebra, number theory, probability theory, and computer science. Much of the mathematics of the factorial function was developed beginning in the late 18th and early 19th centuries.Stirling's approximation provides an accurate approximation to the factorial of large numbers, showing that it grows more quickly than exponential growth. Legendre's formula describes the exponents of the prime numbers in a prime factorization of the factorials, and can be used to count the trailing zeros of the factorials. Daniel Bernoulli and Leonhard Euler interpolated the factorial function to a continuous function of complex numbers, except at the negative integers, the (offset) gamma function. Many other notable functions and number sequences are closely related to the factorials, including the binomial coefficients, double factorials, falling factorials, primorials, and subfactorials. Implementations of the factorial function are commonly used as an example of different computer programming styles, and are included in scientific calculators and scientific computing software libraries. Although directly computing large factorials using the product formula or recurrence is not efficient, faster algorithms are known, matching to within a constant factor the time for fast multiplication algorithms for numbers with the same number of digits. (Wikipedia).
👉 Learn all about factorials. Factorials are the multiplication of a number in descending integer values back to one. Factorials are used often in sequences, series, permutations, and combinations. Factorial quotient expressions are simplified by canceling out common integer products or
From playlist Sequences
Simplifying a factorial divided by another factorial
👉 Learn all about factorials. Factorials are the multiplication of a number in descending integer values back to one. Factorials are used often in sequences, series, permutations, and combinations. Factorial quotient expressions are simplified by canceling out common integer products or
From playlist Sequences
Ex 2: Simplify Expressions with Factorials Containing Variables
This video provides three examples of how to evaluate factorials and how to simplify expression involving factorials. Site: http://mathispower4u.com
From playlist Using the Binomial Theorem / Combinations
Algebra - Ch. 6: Factoring (2 of 55) What is Factoring?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is factoring. Factoring is the process of taking a number or an expression and writing it as a product of it's factor. (It is the reverse of applying the distributive property.) To donat
From playlist ALGEBRA CH 6 FACTORING
But Why Does 0 Factorial Equal 1
Start your free 7 day trial with Blinkist and get 25% off of Premium membership: https://www.blinkist.com/bri Why does 0 factorial = 1 ? Let's answer this question! ►BECOME A CHANNEL MEMBER https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join ►WEBSITE https://www.brithemathgu
From playlist Fun and Amazing Math
Today, we define the factorial of a matrix using the pi function and power series.
From playlist Linear Algebra
👉Learn how to factor quadratics. A quadratic is an algebraic expression having two as the highest power of its variable(s). To factor an algebraic expression means to break it up into expressions that can be multiplied together to get the original expression. To factor a quadratic with th
From playlist Factor Quadratic Expressions
Introduction into factoring quadratics
👉Learn how to factor quadratics. A quadratic is an algebraic expression having two as the highest power of its variable(s). To factor an algebraic expression means to break it up into expressions that can be multiplied together to get the original expression. To factor a quadratic with th
From playlist Factor Quadratic Expressions
All about FACTORIAL | PERMUTATION SERIES | CREATA CLASSES
This is the 2nd video under the PERMUTATION series. This video covers the concept of factorial in full detail. The fundamentals of factorials are covered using Animation & Visual Tools. Visit our website: https://creataclasses.com/ For a full-length course on PERMUTATION, COMBINATION &
From playlist PERMUTATION
This precalculus video tutorial provides a basic introduction into factorials. It explains how to simplify factorial expressions as well as how to evaluate factorial expressions. It discusses how to add and subtract factorials as well as how to multiply and divide factorials. It also ex
From playlist New Precalculus Video Playlist
North Macedonian Math Olympiad | 2019 Q4
We solve a nice problem that combines number theory with a functional relationship. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolph College Math: http
From playlist Math Contest Problems
Croatian Mathematical Olympiad | 2005 Q11.1
We solve a nice number theory problem from the 2005 Croatian Mathematical Olympiad. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathematics/ Randolph Coll
From playlist Math Contest Problems
7! Numbers get very LARGE Fast!
TabletClass Math: https://tcmathacademy.com/ A quick lesson on factorial. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes: https://tabletclass-mat
From playlist GED Prep Videos
A-Level Maths D1-03 [nCr: Simplifying nCr Expressions]
Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/ Many, MANY thanks to Dean @deanencoded for designing my openin
From playlist A-Level Maths D1: Binomial Expansion
How to Compute Binomial Coefficients
How to Compute Binomial Coefficients If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com My FaceBook Page: https://www.facebook.com/themathsorcerer There are several ways that you can help support my chann
From playlist Probability and Counting
Creating loops of numbers by finding and adding the factorial of each digit.
From playlist Math Play
In this Problem of the Week video, Chloe explains how to prove two properties of binomial coefficients. For the full problem and solution transcript, visit our blog: http://bit.ly/1QfZgRd
From playlist Center of Math: Problems of the Week
Discrete Math II - 6.5.2 Permutations with Indistinguishable Objects
We continue our study of enumeration by examining permutations with objects that are identical. The most common example is in permutating the letters of a word where some letters are repeated. Video Chapters: Intro 0:00 Reminder: Permutations with Repetition (Distinct Objects) 0:08 Under
From playlist Discrete Math II/Combinatorics (entire course)
Learn how to factor a perfect square trinomial to a binomial squared
👉Learn how to factor quadratics. A quadratic is an algebraic expression having two as the highest power of its variable(s). To factor an algebraic expression means to break it up into expressions that can be multiplied together to get the original expression. To factor a quadratic with th
From playlist Factor Quadratic Expressions