Integer sequences | Large integers | Factorial and binomial topics | Exponentials
The exponential factorial is a positive integer n raised to the power of n โ 1, which in turn is raised to the power of n โ 2, and so on and so forth in a right-grouping manner. That is, The exponential factorial can also be defined with the recurrence relation The first few exponential factorials are 1, 1, 2, 9, 262144, etc. (sequence in the OEIS). For example, 262144 is an exponential factorial since Using the recurrence relation, the first exponential factorials are: 111 = 121 = 232 = 949 = 2621445262144 = 6206069878...8212890625 (183231 digits) The exponential factorials grow much more quickly than regular factorials or even hyperfactorials. The number of digits in the exponential factorial of 6 is approximately 5ร10183230. The sum of the reciprocals of the exponential factorials from 1 onwards is the following transcendental number: This sum is transcendental because it is a Liouville number. Like tetration, there is currently no accepted method of extension of the exponential factorial function to real and complex values of its argument, unlike the factorial function, for which such an extension is provided by the gamma function. But it is possible to expand it if it is defined in a strip width of 1. (Wikipedia).
Using one to one property when exponents do not have the same base, 25^(x+3) = 5
๐ Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Solving an exponential equation using the one to one property 16^x + 2 = 6
๐ Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations with Logarithms
Solving an equation using the one to one property of exponents 5^(x+1) = 125^x
๐ Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Rewriting a exponential equation to solve using one to one properties (2/3)^x = 4/9
๐ Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
In this video, I define the exponential derivative of a function using power series, and then show something really neat: For โmostโ functions (those that have a power series expansion), the exponential derivative is just shifting the function by 1! I also derive the product rule for exp
From playlist Calculus
Introduction to the Matrix Exponential
In this video we introduce the concept of the matrix exponential. This is similar to the standard exponential function except it operates on matrices. We define the matrix exponential and look at several properties of the matrix exponential that will be very useful in solving systems of
From playlist Ordinary Differential Equations
Worldwide Calculus: The Exponential Function
Lecture on 'The Exponential Function' from 'Worldwide Differential Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for APยฎ
Solve an exponential equation by taking the log of both sides
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From playlist Solve Exponential Equations
Solving exponential equations using the one to one property
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PreCalculus - Exponential Function (9 of 13) Slope of an Exponential Function
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain how the slope of an exponential function is the exponential function. Next video in the Exponential Function can be seen at: http://youtu.be/LDmyh-Dxngs
From playlist Michel van Biezen: PRECALCULUS 1-5 - ALGEBRA REVIEW
Become a Linear Algebra Pro by trying out Brilliant! =D https://brilliant.org/FlammableMaths Complex Numbers but Different Playlist: https://www.youtube.com/playlist?list=PLN2B6ZNu6xmcg3R4wfUlIxtfgtr-2GYAm Today we are going to take the factorial of a matrix and see what we are going to g
From playlist Linear Algebra
Solving an exponential equation using the one to one property
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How to Find the Limit of Almost Any Sequence in Calculus(Examples with n!, n^n, 2^n, ln(n), n^2,...)
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to Find the Limit of Almost Any Sequence in Calculus(Examples with n!, n^n, 2^n, ln(n), n^2,...)
From playlist Calculus 2 Exam 4 Playlist
Solving an exponential equation by taking the log of both sides
๐ Learn how to solve exponential equations in base e. An exponential equation is an equation in which a variable occurs as an exponent. e is a mathematical constant approximately equal to 2.71828. e^x is a special type of exponential function called the (natural) exponential function To s
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Introduction to Resurgence, Trans-series and Non-perturbative Physics - I by Gerald Dunne
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
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Euler's Formula for the Quaternions
In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex
From playlist Math
PreCalculus - Exponential Function (8 of 13) Exponential Function as an Infinite Series
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From playlist Michel van Biezen: PRECALCULUS 1-5 - ALGEBRA REVIEW
Definition of complex exponential function using Taylor series. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org/learn/differential-equations-engineers Vector Calcu
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Solve an exponential equation using one to one property and isolating the exponent
๐ Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations with Logarithms