Register to reply

Moment problem

by zetafunction
Tags: moment
Share this thread:
Nov11-09, 12:31 PM
P: 399
given the set of moments [tex] m_k [/tex]

obtained from the known measure w(x) [tex] \int _{-\infty}^{\infty}dx w(x) x^{k} = m_k [/tex]

now if we define the moment generating function [tex] f(z)= \sum_{k=0}^{\infty} m_{k}(-1)^{k}z^{k} [/tex] , which have the integral representation

[tex] f(z)= \int _{-\infty}^{\infty} \frac{w(x)}{1+xz } [/tex]

my question is , how could i expand f(z) knowing the moment m_k in the form of a continued fraction

[tex] f(z) = a_0 (z)+ \frac{1 \mid}{\mid a_1 (z)} + \frac{1 \mid}{\mid a_2 (z)} + \frac{1 \mid}{\mid a_3 (z)}. [/tex]

where the a_n are Polynomials of degree 1 .

for example for the case of exponential integral , how did euler manage to get the continued fraction ?? thanks.
Phys.Org News Partner Science news on
Security CTO to detail Android Fake ID flaw at Black Hat
Huge waves measured for first time in Arctic Ocean
Mysterious molecules in space

Register to reply

Related Discussions
Moment of Inertia Problem Introductory Physics Homework 2
Moment problem Advanced Physics Homework 2
Moment of Inertia Problem Introductory Physics Homework 5
Moment problem Mechanical Engineering 2
A problem in moment Introductory Physics Homework 1