Regularized Hypergeometric Function and Hypergeometric Function Syntax

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Hi MatLab have the same Syntax for both Hypergeometric Function and Regularized Hypergeometric Function;
BUT they are not the same, so How can you differentiate between them?

Accepted Answer

Antonio Ribeiro
Antonio Ribeiro on 17 May 2014
I think you don't need this answer anymore but in order to clarify future queries about this, one could check the hypergeometric definitions in NIST .
In particular, for scalar a and b, the confluent hypergeometric function is defined as 1F1(a;b;z) and its regularized form is given by 1~F1(a;b;z) = 1F1(a;b;z) / gamma(b) (see NIST eq. (13.2.4)). In this reference 1F1(a;b;z) is represented as M(a;b;z) and 1~F1(a;b;z) is M(a;b;z) with M in bold. In MATLAB, 1F1(a;b;z) is called by
>> hypergeom(a,b,z)
and its regularized form is
>> hypergeom(a,b,z) / gamma(b)
a, b, z can be either numeric or symbolic.
For scalar a, b, and c, the gauss hypergeometric function is defined as 2F1(a,b;c;z) and its regularized form is given by 2~F1(a,b;c;z) = 2F1(a,b;c;z) / gamma(c) (see NIST eq. (15.1.2) and eq. (15.2.2)). In MATLAB:
>> hypergeom([a,b],c,z) % 2F1
>> hypergeom([a,b],c,z) / gamma(c) % 2F1 regularized.
For generalized forms of the hypergeometric function, see definition given in NIST eq. (16.2.5). For usage examples see the Documentation Center page Mathworks .

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