Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.cb2v)

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=29/8, b>=a

For fixed z and a=29/8, b=41/8

http://functions.wolfram.com/07.23.03.cb2v.01

Input Form

Hypergeometric2F1[29/8, 41/8, -(23/4), z] == (307648 - 5320304 z + 45200760 z^2 - 257188415 z^3 + 1154003333 z^4 - 4851207699 z^5 + 28429898497 z^6 + 140485790067 z^7 + 88548349599 z^8 + 10379639823 z^9 + 9688803 z^10 + (1/Sqrt[1 - z]) (307648 - 5474128 z + 47822456 z^2 - 279142985 z^3 + 1277267947 z^4 - 5398686449 z^5 + 30725699719 z^6 + 441536891745 z^7 + 474409879617 z^8 + 110002557813 z^9 + 3478280277 z^10 - 38755212 z^11))/ (307648 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + z)^14)

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]