Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8x0)

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=-41/8, b>=a

For fixed z and a=-41/8, b=-5/8

http://functions.wolfram.com/07.23.03.b8x0.01

Input Form

Hypergeometric2F1[-(41/8), -(5/8), 23/4, z] == (16 2^(3/4) (4 (1150050 - 16062365 z + 111966080 z^2 - 561590325 z^3 + 54781429396 z^4 + 40122954617 z^5 - 2354077656 z^6 + 431736297 z^7 - 59240670 z^8 + 4117680 z^9) + (1/Sqrt[1 - z]) (-4600200 + 66549560 z - 479414025 z^2 + 2462549790 z^3 + 193521997609 z^4 - 105147462324 z^5 - 102672343431 z^6 + 14511709230 z^7 - 2571733809 z^8 + 334708560 z^9 - 21960960 z^10)))/ (6619499979183 (1 + Sqrt[1 - z])^(3/4) 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]