## HTML File #6

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Some Fancy Math Equations...

# Some Fancy Math Equations...

## Abstract

Some Fancy Math Stuff....

Some Fancy Math

First, we have:

ni+1 =

 3ni+1
 if ni 1 \pmod2
 ni / 2
 if ni 0 \pmod2

Second, we have:

 f(z) = n 3 0 fnzn, ^f (z) = n 3 0 fn zn n! .

Third, we have:

 Mn = - 1 2 n+2 k = [(n+2)/2] (-1)k 1/2 k k n+2-k 22k-n-2 3n+2-k.
(1)

Fourth, we have:

 Mn = - 1 2 n+2 k = [(n+2)/2] (-1)k 1/2 k k n+2-k 22k-n-2 3n+2-k.
(2)

Fifth, we have:

M(z) = (1-z-[(1-2z-3z2)])/(2z2)

Sixth, we have:

 I(n,x) = x 0 dt 1 + tn

Seventh, we have:

 .x 1  =  Ku - 1 t (x1-T) .x 2  =  x3 .x 3  =  g Wa W (1- T x1 )-1- m W x3
(3)

Eighth, we have:

 8000 Tt y3 - 400(T +Kt u) y22 - 40 ( m (Kt u +T) y1 + 200 Kt u + 10 m Tt) y2- m2(Kt u +T) y12 +400 mKt uy1+40000(T-Kt u)   =  0
(4)

Nineth, we have:

The discriminant disc(e1,*,en) of n elements e1,*,en L(x,y) is defined as:

 Tr(e1e1)
 *
 Tr(e1en)
 :
 :
 Tr(ene1)
 *
 Tr(enen)

where Tr stands for the trace map of the extension L(x) L(x,y)

Tenth, we have:

 t = 1 L((  (x-a)[1/t] ))

Eleventh, we have:

 h = h x x + h y y + h a a + h b b
 h
 =
cos(x)y·

 1
 0

+sin(x)·

 0
 1

+ 2 a b·

 [(a)/(x)]
 [(a)/(y)]

+ a2·

 [(b)/(x)]
 [(b)/(y)]

(5)
 =

 cos(x)y+2 a b· da[1]+a2·db[1]
 sin(x)+2 a b·da[2] +a2·db[2]

(6)

Twelfth, we have:

p- ea

[1/2]
b- g
 n k !

R O A D M A P

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