- #1

- 75

- 0

Where do the Bernoulli numbers come in?

- Thread starter Piano man
- Start date

- #1

- 75

- 0

Where do the Bernoulli numbers come in?

- #2

- 1,796

- 53

http://www.mathhelpforum.com/math-help/f25/power-series-tangent-function-108861.html

- #3

- 75

- 0

I was expecting something yucky, and this doesn't disappoint...

Thanks for the link :)

Thanks for the link :)

- #4

- 64

- 0

Piano man. Here is a link in http://www.voofie.com/concept/Mathematics/" [Broken] that you maybe interested.

http://www.voofie.com/content/117/an-explicit-formula-for-the-euler-zigzag-numbers-updown-numbers-from-power-series/" [Broken]

I derived the power series of the function sec x + tan x. For the tan x power series, you just take the odd terms from the expansion, since tan x is an odd function. While sec x corresponds to the even terms from the power series, as sec x is even.

It doesn't really show how Bernoulli numbers enter the expression, but it derives an explicit form for Bernoulli numbers.

http://www.voofie.com/content/117/an-explicit-formula-for-the-euler-zigzag-numbers-updown-numbers-from-power-series/" [Broken]

I derived the power series of the function sec x + tan x. For the tan x power series, you just take the odd terms from the expansion, since tan x is an odd function. While sec x corresponds to the even terms from the power series, as sec x is even.

It doesn't really show how Bernoulli numbers enter the expression, but it derives an explicit form for Bernoulli numbers.

Last edited by a moderator:

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 4K

- Last Post

- Replies
- 5

- Views
- 16K

- Last Post

- Replies
- 16

- Views
- 2K

- Last Post

- Replies
- 23

- Views
- 5K

- Last Post

- Replies
- 2

- Views
- 3K

- Last Post

- Replies
- 4

- Views
- 660

- Last Post

- Replies
- 9

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 2K