Potential series method


by matematikuvol
Tags: method, potential, series
matematikuvol
matematikuvol is offline
#1
Dec19-12, 12:44 PM
P: 192
Why sometimes we search solution of power series in the way:
[tex]y(x)=\sum^{\infty}_{n=0}a_nx^n[/tex]
and sometimes
[tex]y(x)=\sum^{\infty}_{n=0}a_nx^{n+1}[/tex]???
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
tiny-tim
tiny-tim is offline
#2
Dec20-12, 05:44 PM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,167
hi matematikuvol!
Quote Quote by matematikuvol View Post
Why sometimes we search solution of power series in the way:
[tex]y(x)=\sum^{\infty}_{n=0}a_nx^n[/tex]
and sometimes
[tex]y(x)=\sum^{\infty}_{n=0}a_nx^{n+1}[/tex]???
no particular reason

sometimes one gives neater equations than the other

they'll both work (provided, of course, that y(0) = 0)
matematikuvol
matematikuvol is offline
#3
Dec21-12, 01:22 AM
P: 192
I think that in the case when
[tex]\alpha(x)y''(x)+\beta(x)y'(x)+\gamma(x)y(x)=0[/tex]
if ##\alpha(0)=0## you must work with ##\sum^{\infty}_{n=0}a_nx^{n+k}##, but I'm not sure.

tiny-tim
tiny-tim is offline
#4
Dec21-12, 03:11 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,167

Potential series method


Quote Quote by matematikuvol View Post
I think that in the case when
[tex]\alpha(x)y''(x)+\beta(x)y'(x)+\gamma(x)y(x)=0[/tex]
if ##\alpha(0)=0## you must work with ##\sum^{\infty}_{n=0}a_nx^{n+k}##, but I'm not sure.
but that's the same as ##\sum^{\infty}_{n=0}b_nx^n## with ##b_n = a_{n-k}## for n ≥ k, and ##b_n = 0## otherwise


Register to reply

Related Discussions
I need a method to calculate ln(x) for small x, other than Taylor series method General Math 12
ODE power series method Calculus & Beyond Homework 10
? Inverse Series method? Calculus 5
Power series method for DE Calculus & Beyond Homework 5
another power series method Calculus & Beyond Homework 2