Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9wj)

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=25/8, b>=a

For fixed z and a=25/8, b=45/8

http://functions.wolfram.com/07.23.03.c9wj.01

Input Form

Hypergeometric2F1[25/8, 45/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (2 (7502416 - 126562496 z + 1046457199 z^2 - 5781114765 z^3 + 25139369577 z^4 - 102449281389 z^5 - 12383482721337 z^6 - 14322904770447 z^7 - 2900300497029 z^8 - 4432600503 z^9 + 128481174 z^10) + (1/Sqrt[1 - z]) (15004832 - 260627408 z + 2217601290 z^2 - 12577983907 z^3 + 55813473805 z^4 - 228713983407 z^5 + 27208977131973 z^6 + 39823473945255 z^7 + 11889287058519 z^8 + 455287315755 z^9 - 12112919571 z^10 + 342616464 z^11)))/(30009664 2^(3/4) (-1 + z)^14)

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]