Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c2s5)

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=9/8, b>=a

For fixed z and a=9/8, b=45/8

http://functions.wolfram.com/07.23.03.c2s5.01

Input Form

Hypergeometric2F1[9/8, 45/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (2 (7502416 - 96879024 z + 588706815 z^2 - 2262744546 z^3 + 6336842925 z^4 - 14826559488 z^5 - 402865932183 z^6 - 9004740810 z^7 + 1687245339 z^8 - 232566340 z^9 + 16085280 z^10) + (1/Sqrt[1 - z]) (15004832 - 201260464 z + 1272417050 z^2 - 5090913953 z^3 + 14800777444 z^4 - 35490705731 z^5 + 982289992762 z^6 + 187568271865 z^7 - 27835845128 z^8 + 5027621819 z^9 - 656815600 z^10 + 42894080 z^11)))/(30009664 2^(3/4) (-1 + z)^12)

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]