Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b71z)

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=-45/8, b>=a

For fixed z and a=-45/8, b=31/8

http://functions.wolfram.com/07.23.03.b71z.01

Input Form

Hypergeometric2F1[-(45/8), 31/8, 23/4, z] == (1/(82744927305 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-36825360 + 91449644 z + 14214031 z^2 + 31413148 z^3 + 174780970 z^4 - 1557769344 z^5 + 3742608303 z^6 - 4498461088 z^7 + 3002112256 z^8 - 1068953600 z^9 + 159318016 z^10 + (1/Sqrt[1 - z]) (36825360 - 109862324 z + 26907621 z^2 - 15176512 z^3 - 153020530 z^4 + 4238319136 z^5 - 15428729499 z^6 + 26509715692 z^7 - 25924107264 z^8 + 14895795200 z^9 - 4713938944 z^10 + 637272064 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]