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

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=-33/8, b>=a

For fixed z and a=-33/8, b=-21/8

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

Input Form

Hypergeometric2F1[-(33/8), -(21/8), 11/2, -z] == (1024 (2 Sqrt[z] (7840 + 137900 z + 1290051 z^2 + 9741004 z^3 + 325290537 z^4 - 1204870758 z^5 + 977590453 z^6 - 198453416 z^7 + 5382111 z^8 + 76342 z^9) Cos[(7 ArcTan[Sqrt[z]])/4] - (8960 + 151440 z + 1366379 z^2 + 10125647 z^3 + 121378803 z^4 - 1571418849 z^5 + 2567275529 z^6 - 1061134011 z^7 + 93821593 z^8 + 267197 z^9) Sin[(7 ArcTan[Sqrt[z]])/4]))/ (435079639771 z^(9/2) (1 + z)^(7/8))

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]