Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7b2)

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=47/8

http://functions.wolfram.com/07.23.03.b7b2.01

Input Form

Hypergeometric2F1[-(45/8), 47/8, -(9/2), z] == (1/10221568) ((1/(1 + Sqrt[z])^(19/4)) (5110784 + 24276224 Sqrt[z] + 83050240 z + 220003280 z^(3/2) + 523014020 z^2 + 1118968653 z^(5/2) + 2301261688 z^3 + 4494352720 z^(7/2) + 8907138240 z^4 + 17357500160 z^(9/2) + 40927158272 z^5 + 8207941632 z^(11/2) - 308893122560 z^6 - 818465669120 z^(13/2) - 922083655680 z^7 - 495503540224 z^(15/2) - 104316534784 z^8) + (1/(1 - Sqrt[z])^(19/4)) (5110784 - 24276224 Sqrt[z] + 83050240 z - 220003280 z^(3/2) + 523014020 z^2 - 1118968653 z^(5/2) + 2301261688 z^3 - 4494352720 z^(7/2) + 8907138240 z^4 - 17357500160 z^(9/2) + 40927158272 z^5 - 8207941632 z^(11/2) - 308893122560 z^6 + 818465669120 z^(13/2) - 922083655680 z^7 + 495503540224 z^(15/2) - 104316534784 z^8))

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]