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User:Mortice/Maths

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Wikipedia:Math

2d

[edit]

My formula:

...where is the r'th integral


The traditional formula:

...where is a Permutation


For example:

Which is the same as:


If you consider:

and:

and:

...then it all logically falls out.

New notation

[edit]

Lets use meaning the expression occurs n times using different variables for a, all summed together.

So .

For instance:

Could be written as:

3d

[edit]

These numbers can be gleaned from the following Pascal's tetrahedron layer:

   1
  3 3
 3 6 3
1 3 3 1

And so...

     1
    4  4
   6 10  6
  4 10 10 4
 1 4  6  4 1