Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b51d)

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=-1/8

http://functions.wolfram.com/07.23.03.b51d.01

Input Form

Hypergeometric2F1[-(47/8), -(1/8), 11/2, z] == (1/(806788224462495 z^(9/2))) (1024 (-2 Sqrt[z] (-7506464 + 101739396 z - 683925999 z^2 + 3314841098 z^3 - 413927267645 z^4 - 75911436576 z^5 + 23846359511 z^6 - 7842099902 z^7 + 1983647589 z^8 - 323874320 z^9 + 25116784 z^10) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) ((60051712 - 855200720 z + 6026048553 z^2 - 30215930392 z^3 + 177715166579 z^4 - 19947070306 z^5 - 173932734529 z^6 + 55077429068 z^7 - 17590018411 z^8 + 4284890302 z^9 - 672865424 z^10 + 50233568 z^11) Sin[ArcSin[Sqrt[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]