Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c90n)

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.c90n.01

Input Form

Hypergeometric2F1[23/8, 43/8, -(17/4), z] == (2 (159120 - 2517840 z + 20101635 z^2 - 114845640 z^3 + 626859429 z^4 - 9103227210 z^5 - 18130681811 z^6 - 5263682116 z^7 - 12075525 z^8 + 439110 z^9) + (1/Sqrt[1 - z]) (318240 - 5194800 z + 42681330 z^2 - 249183345 z^3 + 1363841388 z^4 - 18806927139 z^5 - 46980701438 z^6 - 19709411799 z^7 - 966042000 z^8 + 33201595 z^9 - 1170960 z^10))/ (318240 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-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]