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

In summary, the hypergeometric function can be represented in the form 2F1=(a,b;c;d) or 3F1=(a,b,c;d;e), depending on the number of parameters in each section. The sections are separated by semicolons and the parameters within a section are separated by commas. There does not seem to be a notation for 2F1 with four parameters.
  • #1
sara_87
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0

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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  • #2
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.
 

1. What is a hypergeometric function?

A hypergeometric function is a mathematical function that is defined as a solution to a certain type of differential equation. It is typically denoted by the symbol F and is used in various fields of mathematics and physics to describe a wide range of phenomena.

2. What is the formula for calculating a hypergeometric function?

The formula for a hypergeometric function can vary depending on the specific type of function being used, but in general it involves a series of mathematical terms and coefficients that are used to represent the function's values at different points.

3. What are the applications of hypergeometric functions?

Hypergeometric functions have numerous applications in mathematics, physics, and engineering. Some common uses include solving problems in statistics, quantum mechanics, and differential equations. They are also used in various areas of research, such as in the study of crystal structures and special functions.

4. Can hypergeometric functions be simplified?

Yes, in some cases, hypergeometric functions can be simplified using certain mathematical techniques. For example, the function may be expressed in terms of simpler functions, or it may be possible to approximate the function using a simpler form. However, not all hypergeometric functions can be simplified, as some are considered to be "special functions" and do not have simpler forms.

5. How are hypergeometric functions related to other types of mathematical functions?

Hypergeometric functions are a type of special function that are related to other types of mathematical functions, such as trigonometric functions, exponential functions, and logarithmic functions. They can also be expressed in terms of other special functions, such as the gamma function or the Bessel function.

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