Generalized Hypergeometric Function (vectorized) 1.0

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] ) [1+x+x.^2; 1+2.*x] %Theoretical answer

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Calculation,  Close,  Divergent,  Mbynbybyq,  Nterms,  Number,  Output,  Outputs,  Severe,  Terms
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