Regularized Hypergeometric Function and Hypergeometric Function Syntax

Hi MatLab have the same Syntax for both Hypergeometric Function and Regularized Hypergeometric Function;

hypergeom(a,b,z)

BUT they are not the same, so How can you differentiate between them?

Thanks

Answer 1

[Antonio Ribeiro]

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 .

[Deema42]

Hello. How can i use this command to write the (2F0) type?