Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c6q4)

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=17/8, b>=a

For fixed z and a=17/8, b=45/8

http://functions.wolfram.com/07.23.03.c6q4.01

Input Form

Hypergeometric2F1[17/8, 45/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (-15004832 + 223441520 z - 1602746538 z^2 + 7508970957 z^3 - 26856722172 z^4 + 86273156151 z^5 + 5843946563910 z^6 + 3421521853659 z^7 + 18255184272 z^8 - 1481755887 z^9 + 72383760 z^10 + (1/Sqrt[1 - z]) (2 (-7502416 + 115471968 z - 856295847 z^2 + 4141675919 z^3 - 15212121651 z^4 + 49427374815 z^5 - 3309004551489 z^6 - 2760170836059 z^7 - 212361586281 z^8 + 13012287789 z^9 - 1029055788 z^10 + 48255840 z^11))))/ (30009664 2^(3/4) (-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]