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

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=47/8

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

Input Form

Hypergeometric2F1[43/8, 47/8, -(21/4), z] == (1/(541632 2^(1/4) (-1 + z)^16)) ((1 + Sqrt[1 - z])^(1/4) (-2 (-135408 + 2972528 z - 33297069 z^2 + 263754200 z^3 - 1797536860 z^4 + 13686160488 z^5 + 504408320482 z^6 + 1112783702184 z^7 + 665107499700 z^8 + 114753351720 z^9 + 4059957475 z^10) + (1/Sqrt[1 - z]) (270816 - 6080464 z + 69532814 z^2 - 560079263 z^3 + 3850864640 z^4 - 29107856596 z^5 + 2339744919644 z^6 + 7885403930646 z^7 + 7002328839408 z^8 + 1955878928220 z^9 + 146939157190 z^10 + 1335568465 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]