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

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=-37/8, b>=a

For fixed z and a=-37/8, b=23/8

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

Input Form

Hypergeometric2F1[-(37/8), 23/8, 23/4, z] == (1/(1950509025 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (2455024 - 11661364 z + 15999503 z^2 + 1952860 z^3 + 6053866 z^4 - 28901792 z^5 + 42082927 z^6 - 30642144 z^7 + 11447040 z^8 - 1757184 z^9 + (1/Sqrt[1 - z]) (-2455024 + 12888876 z - 21523307 z^2 + 4742660 z^3 - 3710434 z^4 + 93737816 z^5 - 222920443 z^6 + 249119536 z^7 - 153471360 z^8 + 50620416 z^9 - 7028736 z^10)))

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]