Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5qo)

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=-47/8, b>=a

For fixed z and a=-47/8, b=45/8

http://functions.wolfram.com/07.23.03.b5qo.01

Input Form

Hypergeometric2F1[-(47/8), 45/8, -(11/2), z] == (1/676831232) ((1/(1 - Sqrt[z])^(21/4)) (338415616 - 1776681984 Sqrt[z] + 5808827136 z - 14765304064 z^(3/2) + 32282398176 z^2 - 63458966844 z^(5/2) + 115786450351 z^3 - 199442467224 z^(7/2) + 329741638512 z^4 - 527859620288 z^(9/2) + 830662280448 z^5 - 1293424484352 z^(11/2) + 2094115831808 z^6 - 3394098757632 z^(13/2) + 4356845273088 z^7 - 3600783245312 z^(15/2) + 1642985422848 z^8 - 312949604352 z^(17/2)) + (1/(1 + Sqrt[z])^(21/4)) (338415616 + 1776681984 Sqrt[z] + 5808827136 z + 14765304064 z^(3/2) + 32282398176 z^2 + 63458966844 z^(5/2) + 115786450351 z^3 + 199442467224 z^(7/2) + 329741638512 z^4 + 527859620288 z^(9/2) + 830662280448 z^5 + 1293424484352 z^(11/2) + 2094115831808 z^6 + 3394098757632 z^(13/2) + 4356845273088 z^7 + 3600783245312 z^(15/2) + 1642985422848 z^8 + 312949604352 z^(17/2)))

Standard Form

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MathML Form

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type='integer'> 1776681984 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 338415616 </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]