Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c6jw)

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=37/8

http://functions.wolfram.com/07.23.03.c6jw.01

Input Form

Hypergeometric2F1[17/8, 37/8, -(19/4), z] == (1/(123424 2^(3/4) (-1 + z)^11)) ((1 + Sqrt[1 - z])^(3/4) (-61712 + 794948 z - 4952185 z^2 + 20600237 z^3 - 70709830 z^4 - 4632745474 z^5 - 2416938709 z^6 - 8880415 z^7 + 402132 z^8 + (1/Sqrt[1 - z]) (-61712 + 825804 z - 5341945 z^2 + 22980818 z^3 - 80438199 z^4 + 5267993896 z^5 + 4018691273 z^6 + 270433770 z^7 - 12298537 z^8 + 536176 z^9)))

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]