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

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=45/8

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

Input Form

Hypergeometric2F1[-(23/8), 45/8, -(11/2), z] == (1/96690176) ((1/(1 - Sqrt[z])^(33/4)) (48345088 - 398846976 Sqrt[z] + 1587971328 z - 4184871680 z^(3/2) + 8400817440 z^2 - 13835712660 z^(5/2) + 19436820945 z^3 - 23718364560 z^(7/2) + 25202452320 z^4 - 23016794240 z^(9/2) + 17467684608 z^5 - 10370021376 z^(11/2) + 4399403008 z^6 - 1159741440 z^(13/2) + 140574720 z^7) + (1/(1 + Sqrt[z])^(33/4)) (48345088 + 398846976 Sqrt[z] + 1587971328 z + 4184871680 z^(3/2) + 8400817440 z^2 + 13835712660 z^(5/2) + 19436820945 z^3 + 23718364560 z^(7/2) + 25202452320 z^4 + 23016794240 z^(9/2) + 17467684608 z^5 + 10370021376 z^(11/2) + 4399403008 z^6 + 1159741440 z^(13/2) + 140574720 z^7))

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]