- #1
LagrangeEuler
- 717
- 20
Question:
Why equations
[tex]x(1-x)\frac{d^2y}{dx^2}+[\gamma-(\alpha+\beta+1)x]\frac{dy}{dx}-\alpha \beta y(x)=0[/tex]
should be solved by choosing
##y(x)=\sum^{\infty}_{m=0}a_mx^{m+k}##
and not
##y(x)=\sum^{\infty}_{m=0}a_mx^{m}##?
How to know when we need to choose one of the forms.
Also when I sum over ##m##, then ##\sum^{\infty}_{m=0}a_mx^{m+k}=y(x,k)##. Right?
Why equations
[tex]x(1-x)\frac{d^2y}{dx^2}+[\gamma-(\alpha+\beta+1)x]\frac{dy}{dx}-\alpha \beta y(x)=0[/tex]
should be solved by choosing
##y(x)=\sum^{\infty}_{m=0}a_mx^{m+k}##
and not
##y(x)=\sum^{\infty}_{m=0}a_mx^{m}##?
How to know when we need to choose one of the forms.
Also when I sum over ##m##, then ##\sum^{\infty}_{m=0}a_mx^{m+k}=y(x,k)##. Right?