Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8se)

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=-21/8

http://functions.wolfram.com/07.23.03.b8se.01

Input Form

Hypergeometric2F1[-(41/8), -(21/8), 23/4, z] == (16 2^(3/4) (4 (67650 - 1301135 z + 13274775 z^2 - 106543830 z^3 + 34602591469 z^4 + 89686803426 z^5 + 52567225065 z^6 + 6571482426 z^7 - 43816527 z^8 + 1301481 z^9) + (1/Sqrt[1 - z]) (-270600 + 5339840 z - 55667545 z^2 + 452091215 z^3 + 129618101811 z^4 + 153579074091 z^5 - 155997180219 z^6 - 119077944915 z^7 - 8756219559 z^8 + 239617113 z^9 - 6941232 z^10)))/ (4291763722767 (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]