In the theory of special functions, Whipple's transformation for Legendre functions, named after Francis John Welsh Whipple, arise from a general expression, concerning associated Legendre functions. These formulae have been presented previously in terms of a viewpoint aimed at spherical harmonics, now that we view the equations in terms of toroidal coordinates, whole new symmetries of Legendre functions arise. For associated Legendre functions of the first and second kind, and These expressions are valid for all parameters and . By shifting the complex degree and order in an appropriate fashion, we obtain Whipple formulae for general complex index interchange of general associated Legendre functions of the first and second kind. These are given by and Note that these formulae are well-behaved for all values of the degree and order, except for those with integer values. However, if we examine these formulae for toroidal harmonics, i.e. where the degree is half-integer, the order is integer, and the argument is positive and greater than unity one obtains and . These are the Whipple formulae for toroidal harmonics. They show an important property of toroidal harmonics under index (the integers associated with the order and the degree) interchange. (Wikipedia).
Concavity and Parametric Equations Example
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Concavity and Parametric Equations Example. We find the open t-intervals on which the graph of the parametric equations is concave upward and concave downward.
From playlist Calculus
How to solve a quadratic using the quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
Learn Excel - Checkmarks in Excel - Podcast 2225
Easy checkmarks in Excel from Jack Whipple Rather than use P in Wingdings 2 font, you can use Icon Sets 1 = Green Checkmark: Done 0 = Empty Circle: Still to Do -1 = Yellow Dash: Not required this year, but keep it on the list for next year To start, Home, Conditional Formatting, Icon Sets,
From playlist Excel General
Linearly Parametrized Curves | Algebraic Calculus One | Wild Egg
Parametrized curves figure prominently in the Algebraic Calculus, and they coincide with de Casteljau Bezier curves. The simplest case are the linearly parametrized curves given by a pair of linear polynomials of polynumbers. This gives us an alternate view of oriented polygonal splines.
From playlist Algebraic Calculus One
Find the complex roots of an equation using the quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | Equation
Minicomputer Part 14: Spinning up the 1970’s 10MB Hard Drive!
We’re back out in the garage, oop, that’s not right… We’re inside with the Centurion enjoying the nice air conditioning and working on the drives! First, an update on the Finch drive, because we may have left it on a bit of a cliffhanger in the last episode. Then, we fire up the big one –
From playlist Centurion Minicomputer
Minicomputer Part 15: We Found the Holy Grail!
Oh man, what a journey to get here. There were ups and downs and at several points, all hope seemed lost. But we’ve done it, we found some long lost software on a removable platter and we got it fully backed up and saved in multiple locations around the world! Now, it doesn’t quite boot ju
From playlist Centurion Minicomputer
The discriminant and finding the solutions using quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
Spaceships | SciShow Tangents Podcast
10....9.... Hey gang, Kids Month is about ready to blast off into space ....8....7....6 but before it does, we have one more topic exploring the childlike wonder of science to cover ....5....4...3 Spaceships! And wouldn't you know it? There's one more seat on our rocket! Climb in! ....2..
From playlist SciShow Tangents
Introduction to Parametric Equations
This video defines a parametric equations and shows how to graph a parametric equation by hand. http://mathispower4u.yolasite.com/
From playlist Parametric Equations
How to Win Games and Beat People - with Tom Whipple
It’s the not the taking part that counts, it’s the winning. Tom Whipple has spoken to preposterously overqualified experts to learn the science behind winning at games. Watch the Q&A here: https://www.youtube.com/watch?v=gy6LU4iQ9M8 Subscribe for regular science videos: http://bit.ly/RiSu
From playlist Ri Talks
High-Speed Collisions in Space – Experiments with a Carrot Gun
Andy uses a carrot gun to discuss the hazards of micrometeoroid impacts in space, showing that at high enough speeds even tiny specks of dust can be dangerous. Why do high energy collisions in space make solid matter behave in a way that's wholly unfamiliar to us? Subscribe for regular sci
From playlist Tales from the Prep Room
Learn to find the solutions of a quadratic by applying the quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
Ona Judge, George Washington's fugitive slave
Ona Judge, like many slaves in eighteenth century America, sought freedom by running away from those who claimed her as property to live life as a fugitive slave, always on the run. The people who were seeking her were George and Martha Washington, the first President of the United States
From playlist History without War
How to use the quadratic formula to solve a quadratic equation
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
Performing a surgery with a playdough
A Whipple surgery, also known as a pancreaticoduodenectomy, is an operation conducted to remove the head of the pancreas, the first part of the small intestine, the gallbladder, and the bile duct, according to the Mayo Clinic. The procedure is most often used to treat pancreatic cancer t
From playlist Engineering Wonders
Solving a quadratic using quadratic formula with two real solutions
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
Q&A - How to Win Games and Beat People - with Tom Whipple
What’s the furthest a paper aeroplane has ever been thrown?What are the chances of someone landing on Go in Monopoly? What’s the least-landed on square? Tom Whipple answers questions from the audience after his talk Watch the talk here: https://www.youtube.com/watch?v=tNoFL3AF69c Subscri
From playlist Ri Talks
Ask Adam Savage: First Job Ever Plus That Charmin Commercial
In this live-stream excerpt, Adam answers questions from Tested members Adam G and Eric Cothern about his work history! Thank you, Adam and Eric, for your questions and support. Join this channel to support Tested and get access to perks, like asking Adam a question: https://www.youtube.co
From playlist Adam Savage's Live Streams
Describe and solve for the zeros using quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c