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

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=33/8

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

Input Form

Hypergeometric2F1[29/8, 33/8, -(19/4), z] == (-2 (-7600 + 115600 z - 871345 z^2 + 4525810 z^3 - 20196875 z^4 + 117227100 z^5 + 525166473 z^6 + 269401602 z^7 + 21094659 z^8) + (1/Sqrt[1 - z]) (15200 - 238800 z + 1856390 z^2 - 9895015 z^3 + 44715580 z^4 - 253619925 z^5 - 3410375754 z^6 - 3146136369 z^7 - 548275896 z^8 - 9688803 z^9))/(15200 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + z)^12)

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]