# Generalized Hypergeometric Function (vectorized) (Scripts) 1.0

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## Generalized Hypergeometric Function (vectorized) (Scripts) Publisher's description

### PFQ Generalized Hypergeometric Function pFq [Y,TT,NTERMS] = PFQ(A,B,Z,D) returns the Generalized Hypergeometric

PFQ Generalized Hypergeometric Function pFq
[Y,TT,NTERMS] = PFQ(A,B,Z,D) returns the Generalized Hypergeometric
Function pFq with numerator parameters A, denominator parameters B,
evaluated at the values in Z, with respect to derivatives D.

PFQ(A,B,Z) returns the values evaluated at Z

Inputs:
A : real or complex valued vector (or empty [])
B : real or complex valued vector (or empty [])
Z : real or complex valued M-by-N-by-... array
D : scalar or vector of real non-negative integers

Outputs:
Y : Evaluation of pFq at values in Z, with respect to derivative D
TT : Estimated Truth Table on values given
+1 : Terms were convergent, answer valid close to precision
0 : Uncharacterized, use answers with caution
-1 : Terms were divergent, use answers with severe caution
NTERMS : Number of terms used in the calculation for each output

If Z is M-by-N-by-... array and D is a vector 1-by-Q then the outputs
will be an array of size M-by-N-by-...-by-Q

Examples:
%0F1: Confluent Hypergeometric Function
pfq( [] , 1 , 1.5 )
pfq( [] , 1+1i , 1.5-1i )
pfq( [] , 1 , -2 )
%1F1: Kummer Confluent Hypergeometric Function
pfq( 1 , 2 , 3 )
pfq( 2+1i , 2, 0.5 )
pfq( 10 , 1/3 , -1 )
%2F1: Hypergeometric Function
pfq( [1/3 1/3] , 2/3 , 1/2 )
pfq( [2+1i -1i] , 3/4 , 0.5-0.5i )
%PFQ: Generalized Hypergeometric Function
pfq( [1 1] , [3 3 3] , 2 )
pfq( [1i 1i 1i] , [2 2 2] , -1i )
pfq( [1 2 3 4] , [5 6 7] , [.1 .3 .5] )

Vectorization with derivatives:
Evaluate pFq above, at [.1 .3 .5], but with respect to the 0th, 1st and
2nd derivative. Show all outputs
[y , tt , nterms] = pfq( [1 2 3 4] , [5 6 7] , [.1 .3 .5] , 0:2 )

Finite degree polynomial, with derivatives
x = [.1 .3 .5];
y = pfq( [1 -2] , -2 , x , [0:4] )

#### System Requirements:

MATLAB 7.12 (2011a)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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