Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c90i)

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=23/8, b>=a

For fixed z and a=23/8, b=43/8

http://functions.wolfram.com/07.23.03.c90i.01

Input Form

Hypergeometric2F1[23/8, 43/8, -(21/4), z] == (-12096 + 195120 z - 1545336 z^2 + 8236539 z^3 - 35367150 z^4 + 154992621 z^5 - 1890115920 z^6 - 3210168379 z^7 - 812835254 z^8 - 1571325 z^9 + 51660 z^10 + (1/Sqrt[1 - z]) (-12096 + 201168 z - 1641384 z^2 + 8985573 z^3 - 39303975 z^4 + 171735921 z^5 - 1963650843 z^6 - 4250434001 z^7 - 1575550053 z^8 - 69934725 z^9 + 2153935 z^10 - 68880 z^11))/(12096 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-1 + z)^13)

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]