I have worked non-stop every day for the past 3 months on a massively difficult generalization of Bell polynomials.  Sufficiently complex examples on Maple might help me to visualize the general case. One published math paper in particular has helped me tremendously.

I have been working on a problem related to and using the famous Hadamard-Weierstrass Factorization Theorem (HWFT) for representing an entire function, E(z), with pre-defined zeroes, a(n), which go off to infinity. From HWFT one can represent any meromorphic function with pre-defined poles and zeroes as the ratio of two entire functions.

I am not interested in creating an entire function, but a function F(z) analytic on a disk centered at a pre-defined point such that the analytic continuation, A(z), of F(z) equals pre-defined values

If I have a set of numbers,

1, 2, 3, 4, 5

for example, how do I compute their mean?

How do I compute their standard deviation?

I am trying to avoid explicitly recopying cutting and pasting

my data over and over again, such as

a:= (1 + 2 + 3 + 4 +5 )/ 5;

sdev: = sqrt( (a-1)^2 + (a-2)^2 etc.

My REAL question is: WHERE in Maple 11 Help is an example shown anywhere of an explicit finite data set of numbers, such as 1, 2, 3, 4,5, or a set of pairs of numbers (2,3), (4,5) etc 

Let w =f(z) = sum of z^(k+a) / (k + a)

where k= 0 to infinity and a is a nonzero parameter.

I need to find the inverse of this series, z = g(w). The powseries examples in Maple Help don't help. They don't work on my example, with a symbolic variable, a, stuck in there.  I hope that if I see about 7 or 8 terms of the inversion, I will get the general pattern.  I have tried to compute the inverse directly from the Lagrange Inversion Formula, but the complexity always grows too quickly for me to complete the solution, no matter which shortcut I try to take.

Since I've been helped so many times on this forum, I wanted to "give back" something to the forum.  I remember several months ago someone on this forum had a coupled system of differential equations to solve: an autonomous systems of ODEs that looked like it came from chemical kinetics, something like:

dx/dt = (5*x + y)/(2*x+3*y+5)

dy/dt = 2*x*y/(7*x+6*y+1)