Could you possibly be any more vague? What is your question? If it refers to another thread, then you need to be posting it in the appropriate thread. If it's a new question then you need to post the whole problem, as well as any work you've done on it.
You don't if you expect someone else to spend all the necessary time collecting the information together. But the chances of someone doing that are rather small. You are more likely to get help if you follow @topsquark's suggestions in post #2, i.e. either post in the relevant thread, or make you post self-contained.
and gave two numbers, without any explanation of what you are trying to do. Now you are saying
Do [imath]y(1)[/imath] mean [imath]y_1(1)[/imath] in one place and [imath]y_2(1)[/imath] in another? If that is the case then your numerical values are different from what I get. In particular both values must be larger than 1.
Ai(1) = 0.13529 and Bi(1) = 1.20742 are Airy function's solutions taken from Wolfram. At least one of them must be the Airy function I derived by Power Series. I don't know if y(1) = 0.13529 and y(1) = 1.20742 means y1(x) and y2(x) respectively. Maybe, Ai(x) = y1(x) + y2(x) and Bi(x) another Airy functions that its answers can be derived from Ai(x). This function comes with two constants a0 and a1. Maybe because I got rid of them, the function has stretched or compressed somehow to give wrong results.
What do you mean by 4 iterations? Does it mean from n = 1 to n = 4? If it does mean this, did you use my infinite series to do the 4 iterations? Can I use Wolfram calculator to do the 4 iterations at once? If yes, how to do that?
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Thank you.
Thank you for clarifying that Ai(x) and Bi(x) are slightly different than my equation. You are right that this infinite series was solved based near zero. Nevertheless its radius of convergence is infinite. The only benefit of finding solutions near zero on this particular infinite series (based near zero) is that the function will converge faster which means we need less indices or iterations (if that is the same meaning) to compute the function.
I was computing the series from your post #8 for [imath]x=1[/imath]. They converge quite fast, but the answers I get are [imath]y_1(1) \approx 1.17230[/imath] and [imath]y_2(1) \approx 1.08534[/imath], and it required only [imath]1 \leq n \leq 4[/imath]. Computing for larger [imath]n[/imath] did not change the result, which means the rest of the sum did not add more than 0.00001.
My solution agrees with yours.
Someone else is going to have to chime in with an "official" answer, but I suspect the difference is that yours is a power series solution and the Ai and Bi are asymptotic solutions.
I will be waiting for this charming someone to fill up the remaining gaps officially.
Instead of waiting I'd concentrate on stating the problem in a clearer way
I don't agree with you on this. Three years ago, I used to state problems in a clear systematic way. Guess what happened? I got banned by Dan. Go back to all my posts in that website and you will see no one single vagueness.Instead of waiting I'd concentrate on stating the problem in a clearer way
You didn't get banned for stating a problem in a clear and concise manner. You got banned because you were rude, didn't follow forum guidelines, and didn't want to do your own work. Pretty much the same reason you've been banned everywhere else.
When you are begging for help - you cannot choose the way the help is given to you.