Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.by5c)

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=1/8, b>=a

For fixed z and a=1/8, b=45/8

http://functions.wolfram.com/07.23.03.by5c.01

Input Form

Hypergeometric2F1[1/8, 45/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (-165053152 + 1804820336 z - 8986072414 z^2 + 26946662105 z^3 - 54350895403 z^4 + 78666808298 z^5 + 86433313772 z^6 - 40515234643 z^7 + 13100220653 z^8 - 2575253328 z^9 + 231628032 z^10 + (1/Sqrt[1 - z]) (2 (-82526576 + 943673456 z - 4933925469 z^2 + 15612205796 z^3 - 33403660643 z^4 + 51484782570 z^5 - 151196437795 z^6 + 80430153232 z^7 - 34415361357 z^8 + 10194783442 z^9 - 1848734848 z^10 + 154418688 z^11))))/ (330106304 2^(3/4) (-1 + z)^11)

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]