Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bpf8)

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=-15/8, b>=a

For fixed z and a=-15/8, b=45/8

http://functions.wolfram.com/07.23.03.bpf8.01

Input Form

Hypergeometric2F1[-(15/8), 45/8, -(19/4), z] == (1/(93290912 2^(3/4) (-1 + z)^8)) ((1 + Sqrt[1 - z])^(3/4) (46645456 - 260846300 z + 511105309 z^2 - 278477836 z^3 - 238053634 z^4 + 2203651712 z^5 - 3269483235 z^6 + 2306103648 z^7 - 825597696 z^8 + 121245696 z^9 + (1/Sqrt[1 - z]) (46645456 - 284169028 z + 635697777 z^2 - 504340044 z^3 - 148222074 z^4 - 2724674760 z^5 + 6576673889 z^6 - 6951780176 z^7 + 4009666176 z^8 - 1238882304 z^9 + 161660928 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]