Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b773)

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=39/8

http://functions.wolfram.com/07.23.03.b773.01

Input Form

Hypergeometric2F1[-(45/8), 39/8, 23/4, z] == (1/(2565092746455 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (257777520 + 73036964 z + 159841591 z^2 + 563916223 z^3 + 4409069665 z^4 - 53872611759 z^5 + 161109068868 z^6 - 231031111168 z^7 + 178937414656 z^8 - 72489697280 z^9 + 12108169216 z^10 + (1/Sqrt[1 - z]) (-257777520 + 55851796 z - 91100919 z^2 - 458754712 z^3 - 4092497110 z^4 + 136326676156 z^5 - 604795817259 z^6 + 1231345867312 z^7 - 1394332203264 z^8 + 911123333120 z^9 - 323256254464 z^10 + 48432676864 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]