Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c7nl)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=19/8, b>=a

For fixed z and a=19/8, b=47/8

http://functions.wolfram.com/07.23.03.c7nl.01

Input Form

Hypergeometric2F1[19/8, 47/8, -(21/4), z] == ((1 + Sqrt[1 - z])^(1/4) (-105889056 + 1651365040 z - 12585170130 z^2 + 64184762665 z^3 - 262039840604 z^4 + 1085803870827 z^5 + 13362061765310 z^6 + 7503298454175 z^7 + 74930594400 z^8 - 5838342147 z^9 + 277520720 z^10 + (1/Sqrt[1 - z]) (2 (-52944528 + 852154784 z - 6698808259 z^2 + 35138772583 z^3 - 146329074847 z^4 + 604762828943 z^5 - 19500156708733 z^6 - 21998200468227 z^7 - 2758934078781 z^8 + 157843378509 z^9 - 12058275284 z^10 + 555041440 z^11))))/(211778112 2^(1/4) (-1 + z)^13)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]