Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bdq8)

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=-29/8

http://functions.wolfram.com/07.23.03.bdq8.01

Input Form

Hypergeometric2F1[-(33/8), -(29/8), 11/2, -z] == -((1024 (Sqrt[z] (-3136 - 62888 z - 684201 z^2 - 6173167 z^3 - 279330909 z^4 + 1316789253 z^5 - 1500072091 z^6 + 516007667 z^7 - 46468191 z^8 + 496223 z^9) Cos[(7 ArcTan[Sqrt[z]])/4] + (1792 + 34704 z + 366343 z^2 + 3260257 z^3 + 48372051 z^4 - 753203451 z^5 + 1637124853 z^6 - 1023405789 z^7 + 187377521 z^8 - 7058777 z^9) Sin[(7 ArcTan[Sqrt[z]])/4]))/ (195035700587 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]