Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.1155)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a=-9/2, b>=a

For fixed z and a=-9/2, b=-9/2

http://functions.wolfram.com/07.23.03.1155.01

Input Form

Hypergeometric2F1[-(9/2), -(9/2), 11/2, z] == (1/(4294967296 z^(9/2))) (3 (Sqrt[(-(-1 + z)) z] (-3675 + 4 z (20650 + z (-258475 + 8 z (349125 + z (38301307 + 16 z (7259372 + 3 z (1832569 + 8 z (46913 + 1793 z)))))))) + 105 (35 + 2 z (-405 + 64 z (81 + 2 z (-441 + 2 z (3969 + 2 z (19845 + 16 z (2205 + 2 z (9 + z) (63 + 2 z)))))))) ArcSin[Sqrt[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]