Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c3jm)

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=11/8, b>=a

For fixed z and a=11/8, b=31/8

http://functions.wolfram.com/07.23.03.c3jm.01

Input Form

Hypergeometric2F1[11/8, 31/8, -(21/4), z] == (1/(525504 2^(1/4) (-1 + z)^10)) ((1 + Sqrt[1 - z])^(1/4) (2 (131376 - 1438880 z + 7339737 z^2 - 23521157 z^3 + 55361000 z^4 - 117193602 z^5 - 380974735 z^6 - 5743769 z^7 + 341214 z^8) + (1/Sqrt[1 - z]) (262752 - 3009136 z + 16085510 z^2 - 54038753 z^3 + 132577819 z^4 - 284680154 z^5 + 3234713372 z^6 + 728776235 z^7 - 47826829 z^8 + 2729712 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]