# Derivation for the indicial exponent in the Frobenius method

• I
• Kloo
In summary, the conversation discussed different perspectives on the topic of climate change. The first person believed that human activity is the main cause of climate change and that urgent action is needed to address it. The second person argued that natural cycles and other factors play a larger role in climate change and that more research is needed before taking action. Overall, the conversation highlighted the complexity of the issue and the need for further discussion and collaboration to find solutions.
Kloo
I'm reading a book called Asymptotic Methods and Perturbation Theory, and I came across a derivation that I just couldn't follow. Maybe its simple and I am missing something. Equation 3.3.3b below. y(x) takes the form A(x)*(x-x0)^α and A(x) is expanded in a taylor series.

Use $$\begin{split} \left(\sum_{n=0}^\infty a_nx^n \right)\left(\sum_{n=0}^\infty b_nx^n \right) &= \sum_{n=0}^\infty \sum_{m=0}^\infty a_n b_m x^{n+m} \\ &=\sum_{k=0}^\infty \left(\sum_{n=0}^n a_n b_{k-n}\right) x^k. \end{split}$$

Kloo

• Differential Equations
Replies
2
Views
3K
• Calculus and Beyond Homework Help
Replies
4
Views
2K
• Calculus and Beyond Homework Help
Replies
7
Views
658
• Differential Equations
Replies
1
Views
1K
• Differential Equations
Replies
1
Views
3K
• Differential Equations
Replies
5
Views
15K
• Differential Equations
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
244
• Calculus and Beyond Homework Help
Replies
2
Views
5K
• Calculus and Beyond Homework Help
Replies
3
Views
579