On Hypergeometric Series and OEIS Sequence

Question

I have been searching an integer sequence in OEIS. The sequence is the following: OEIS A321234 (https://oeis.org/A321234) . So far, so good. However, this sequence is the denominator of a Hypergeometric Series, the following one:
$${}_3 F_2([1/2, 1, 1], [3/2, 3/2], x).$$
The problem is: I do not even know what those kind of series are. Do not even know what this notation means. Could someone recomend me any book references so as to understand it better? I have read Wiki's page, but it seems not enough.
Thanks a lot

Claude Leibovici · Answer

$$, _3F_2left(frac{1}{2},1,1;frac{3}{2},frac{3}{2};xright)$$ is one of the many hypergeometric functions (google for that).
They are very special functions corresponding to infinite sums. For this one, the first terms of its expansion are
$$1+frac{2 x}{9}+frac{8 x^2}{75}+frac{16 x^3}{245}+frac{128 x^4}{2835}+frac{256
   x^5}{7623}+frac{1024 x^6}{39039}+frac{2048 x^7}{96525}+frac{32768
   x^8}{1859715}+Oleft(x^{9}right)$$
You would find the numerators in sequence $A046161$

On Hypergeometric Series and OEIS Sequence

One Answer

Add your own answers!

Ask a Question