What is the notation for hypergeometric functions and what does it represent?

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SUMMARY

The notation for hypergeometric functions is defined as 2F1=(a,b;c;d), where the first two parameters (a, b) are separated by a comma, and the third (c) and fourth (d) parameters are separated by a semicolon. There is no valid notation for 2F1=(a,b,c;d). The structure of hypergeometric functions includes a specific number of parameters in each section, with the first number indicating the count of parameters before the F and the second number indicating those after. For example, 3F1(a, b, c; d; e) follows the same notation rules.

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Homework Statement



I have seen some hypergeometric function in the form:

2F1=(a,b;c;d),

Is there such thing as:
2F1=(a,b,c;d)

Homework Equations





The Attempt at a Solution



I don't understand why sometimes we have a comma and sometimes we have a semi-colon.

thank you
 
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This isn't anything that I know about, so I'll defer to Wikipedia: http://en.wikipedia.org/wiki/Hypergeometric_function
See especially the Notation section.

Based on my reading of that section, I don't think there is anything such as 2F1(a, b, c;d). I think you might have something like this: 3F1(a, b, c;d;e). Apparently the first number (the one before F) represents the number of parameters in the first position. The second number represents the number of parameters in the second section. The three sections are separated by semicolons, and the parameters within a section are separated by commas.

That's how it seems to me, FWIW.
 

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