Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6ka)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-1/8

http://functions.wolfram.com/07.23.03.b6ka.01

Input Form

Hypergeometric2F1[-(45/8), -(1/8), 23/4, z] == (1/(2565092746455 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (6609680 - 89561164 z + 594262809 z^2 - 2735534098 z^3 + 12605062135 z^4 + 94902348024 z^5 - 1282145833 z^6 + 400539158 z^7 - 100138711 z^8 + 16370480 z^9 - 1277696 z^10 + (1/Sqrt[1 - z]) (-6609680 + 92866004 z - 638217181 z^2 + 3021883462 z^3 - 13903885715 z^4 - 8748786716 z^5 + 24891324109 z^6 - 6199673322 z^7 + 1872368659 z^8 - 445154420 z^9 + 68995584 z^10 - 5110784 z^11)))

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]