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

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=-25/8, b>=a

For fixed z and a=-25/8, b=35/8

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

Input Form

Hypergeometric2F1[-(25/8), 35/8, -(9/2), z] == (1/1050624) ((1/(1 - Sqrt[z])^(23/4)) (525312 - 3020544 Sqrt[z] + 8769792 z - 18144240 z^(3/2) + 30564540 z^2 - 44376039 z^(5/2) + 57053808 z^3 - 65319264 z^(7/2) + 65773440 z^4 - 55376640 z^(9/2) + 34670592 z^5 - 13471744 z^(11/2) + 2342912 z^6) + (1/(1 + Sqrt[z])^(23/4)) (525312 + 3020544 Sqrt[z] + 8769792 z + 18144240 z^(3/2) + 30564540 z^2 + 44376039 z^(5/2) + 57053808 z^3 + 65319264 z^(7/2) + 65773440 z^4 + 55376640 z^(9/2) + 34670592 z^5 + 13471744 z^(11/2) + 2342912 z^6))

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]