Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9433)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=-1/4

http://functions.wolfram.com/07.23.03.9433.01

Input Form

Hypergeometric2F1[-(23/4), -(1/4), 3/2, -z] == (1/(49725 Sqrt[z] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[2] (-4807 + 56896 z + 12070 z^2 + 8252 z^3 + 3961 z^4 + 1132 z^5 + 144 z^6 + (4807 - 29630 z - 55622 z^2 - 36088 z^3 - 22313 z^4 - 9602 z^5 - 2480 z^6 - 288 z^7)/Sqrt[1 + z]))

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]