Hi all, I am trying to find the functions F(x) and f(x), if it is possible.

I have one row of data in the style:


Ak
Ak-1
.
.
.
A3
A2
A1
A0


I also have:

A0= F(1)+ F(2)+ F(3)+... F(k)
A1= F(2)+ F(3)+ F(4)+... F(k)
you write this as if the number of summands on the right would be the

.
.
.
etc

F(x)= (1/x)* f(Ax)

F(1)> F(2)> F(3)> ...> F(K) <=
=> f(A1)> (1/2)*f(A2)> (1/3)*f(A3)>...> (1/k)*f(Ak)


A0= F(1)+ F(2)+ F(3)+ ... + F(k) =

=> A0= f(A1)+ (1/2)*f(A2)+ (1/3)f(A3)+... + (1/k)*f(Ak)


A1= f(A2)+ (1/2)*f(A3)+... + (1/(k-1))*f(Ak)


A0- A1= f(A1)- (1/2)*f(A2)- (1/6)*f(A3)- (1/12)*f(A4)- ... -( 1/( ( k(k-1) ) )*f(Ak) =

k
=> f(A1)= A0 - A1 + S( (1/( v*(v-1) ))* f(Av) ) [where S means sum].
n=2


How may I find the "body" of f(x) and F(x), if it is possible?

In article <1173548684.181728@athprx03>,
John Nore <j...@no.spam> writes:
Hi all, I am trying to find the functionsF(x) andf(x), if it is possible.

I have one row of data in the style:


Ak
Ak-1
.
.
.
A3
A2
A1
A0


I also have:

A0=F(1)+F(2)+F(3)+...F(k)
A1=F(2)+F(3)+F(4)+...F(k)
you write this as if the number of summands on the right would be the
same but they aren't , or his there a typo?
Ak=F(k) ??????

.
.
.
etc


henceF(i)=A(i)-A(i-1) i=1,...,k


F(x)= (1/x)*f(Ax)

hence i*F(i)=f(Ai) = i*(A(i)-A(i-1)) i=1,...,k

you have the data A0,..,Ak
and want to know how the functionf(.) might look like?
no knowledge of any other kind?
f(.) could indeed be an arbitrary combination of almost
arbitrary functions
then it depends on your later uses off(.) what to do
maybe you look at the graph and decide on this,
whether to "fit" the data list (i,f(Ai)) by some suitable linear
combination
or you use an interpolating spline or whatever

hth
peter


F(1)>F(2)>F(3)> ...>F(K) <=
=>f(A1)> (1/2)*f(A2)> (1/3)*f(A3)>...> (1/k)*f(Ak)


A0=F(1)+F(2)+F(3)+ ... +F(k) =

=> A0=f(A1)+ (1/2)*f(A2)+ (1/3)f(A3)+... + (1/k)*f(Ak)


A1=f(A2)+ (1/2)*f(A3)+... + (1/(k-1))*f(Ak)


A0- A1=f(A1)- (1/2)*f(A2)- (1/6)*f(A3)- (1/12)*f(A4)- ... -( 1/( ( k(k-1) ) )*f(Ak) =

k
=>f(A1)= A0 - A1 + S( (1/( v*(v-1) ))*f(Av) ) [where S means sum].
n=2


How may I find the "body" off(x) andF(x), if it is possible?