Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b88l)

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=-43/8, b>=a

For fixed z and a=-43/8, b=41/8

http://functions.wolfram.com/07.23.03.b88l.01

Input Form

Hypergeometric2F1[-(43/8), 41/8, -(11/2), z] == (1/4055040) ((1/(1 - Sqrt[z])^(21/4)) (2027520 - 10644480 Sqrt[z] + 32774400 z - 77817600 z^(3/2) + 157309600 z^2 - 284913300 z^(5/2) + 475738725 z^3 - 746201500 z^(7/2) + 1112403600 z^4 - 1589702400 z^(9/2) + 2187144960 z^5 - 2905943040 z^(11/2) + 3690086400 z^6 - 3995729920 z^(13/2) + 3054305280 z^7 - 1359740928 z^(15/2) + 258998272 z^8) + (1/(1 + Sqrt[z])^(21/4)) (2027520 + 10644480 Sqrt[z] + 32774400 z + 77817600 z^(3/2) + 157309600 z^2 + 284913300 z^(5/2) + 475738725 z^3 + 746201500 z^(7/2) + 1112403600 z^4 + 1589702400 z^(9/2) + 2187144960 z^5 + 2905943040 z^(11/2) + 3690086400 z^6 + 3995729920 z^(13/2) + 3054305280 z^7 + 1359740928 z^(15/2) + 258998272 z^8))

Standard Form

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MathML Form

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77817600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 32774400 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 10644480 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2027520 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]