Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bd4u)

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=-35/8, b>=a

For fixed z and a=-35/8, b=33/8

http://functions.wolfram.com/07.23.03.bd4u.01

Input Form

Hypergeometric2F1[-(35/8), 33/8, -(7/2), -z] == (1/(21760 (1 + z)^(21/8))) ((-(-21760 + 72080 z - 196605 z^2 + 620925 z^3 - 4120800 z^4 + 16628480 z^5 + 49786880 z^6 + 28114944 z^7)) Cos[(5 ArcTan[Sqrt[z]])/4] + 2 Sqrt[z] (13600 - 42500 z + 114495 z^2 - 365160 z^3 + 16309568 z^4 + 34411520 z^5 + 17571840 z^6) Sin[(5 ArcTan[Sqrt[z]])/4])

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]