Seem to remember reading about RF experimenting with non-integer differentiation. I found it quite interesting to play with.
I started with 'half' differentiation.
e.g. f(x) = x^2 , D[1]f = 2x , D[2]f = 2
but what about non-integer diff?
e.g. D[0.5]f = px^1.5
what is p?
Clearly...
I really need someone to answer this by tomorrow 12/01 10:50 am pacific time...
1) Derive the following, for any integer k.
infinity
SUM OF: 1/(n^(2k)) = ((2(pi))^(2k)(-1)^(k+1)B2k ) /(2(2k)!)
n=1
where Bn is defined by the following, for |x| < 2(pi).
````````````infinity
(x)/(e^(x)-1)...
if
a^k =1
and
a \in \mathbb{C}
k \in Z^+
and for some k
A = \{a|a^k = 1\}
does
|A| = k
?
edited: becasue the real numbers are a subset of the complex numbers