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http://img280.echo.cx/img280/9528/solution9lx.gif

Thanks

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In summary, The conversation is about verifying a mathematical solution and determining the radius of convergence for a given series. It is mentioned that the solution is correct and the class got the same result. The formula being discussed is a Bessel function of the first kind.

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http://img280.echo.cx/img280/9528/solution9lx.gif

Thanks

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[tex] \sum_{k=1}^{\infty} (-1)^{k}\frac{x^{2k}}{4^{k}(k!)^{2}} =-\frac{x^{2}}{4}\ _{2}F_{1} \left(1,2,2;-\frac{x^{2}}{4}\right) [/tex]

Daniel.

- #3

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there was no need to take the x's ...take x^2=w and just take the limit of the ratio's..

As per my knowledge it seems to me R is infinite

- #4

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Well,try x=60.How big is the number...?

Daniel.

Daniel.

- #5

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I have left it as R = infinity; seems the rest of the class got the same thing. So I'll just leave it at that

- #6

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dextercioby said:It doesn't converge for every possible "x",as your "radius of convergence =infinite" might mean.

[tex] \sum_{k=1}^{\infty} (-1)^{k}\frac{x^{2k}}{4^{k}(k!)^{2}} =-\frac{x^{2}}{4}\ _{2}F_{1} \left(1,2,2;-\frac{x^{2}}{4}\right) [/tex]

You've missed the k=0 term, though this doesn't affect convergence. The OP's work is fine.

For interests sake, this thing is a Bessel function of the first kind (it's a solution to the d.e. xy''+y'+xy=0).

The process for verifying a math problem involves carefully examining the problem, identifying the given information and what is being asked, and then applying the appropriate mathematical concepts and operations to arrive at a solution. Once a solution is obtained, it should be checked using alternative methods or through estimation to ensure accuracy.

Some common mistakes when verifying a math problem include misinterpreting the given information, using incorrect mathematical formulas or operations, and making calculation errors. It is important to double-check each step and the final solution to catch any mistakes.

If the solution to a math problem does not match the answer provided, it is important to go back and review the steps and calculations. Look for any errors or misunderstandings and try to correct them. If the discrepancy cannot be resolved, it may be necessary to seek help from a teacher or tutor.

To improve your ability to verify math problems, it is important to practice regularly and seek help when needed. It can also be helpful to break down the problem into smaller, more manageable steps and to check your work at each stage. Additionally, staying organized and keeping track of your work can help to catch any mistakes.

When verifying more complex math problems, it can be helpful to draw diagrams or visualize the problem to gain a better understanding. It is also important to carefully read and identify the given information and to use multiple methods or approaches to solving the problem. Don't be afraid to ask for help or collaborate with others to find a solution.

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