Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bco1)

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=-35/8, b>=a

For fixed z and a=-35/8, b=-1/8

http://functions.wolfram.com/07.23.03.bco1.01

Input Form

Hypergeometric2F1[-(35/8), -(1/8), 5, z] == (1/(48511109960775 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-16 (102144 - 1171464 z + 6723948 z^2 - 30306045 z^3 - 475828838 z^4 - 8130590 z^5 + 2026740 z^6 - 370005 z^7 + 33150 z^8) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-51072 + 548625 z - 2966964 z^2 - 480446274 z^3 - 30389540 z^4 + 7691905 z^5 - 1440240 z^6 + 132600 z^7) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 8 (102144 - 1171464 z + 6723948 z^2 - 30306045 z^3 - 475828838 z^4 - 8130590 z^5 + 2026740 z^6 - 370005 z^7 + 33150 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-51072 + 577353 z - 3269805 z^2 + 310732422 z^3 + 110629030 z^4 - 16344395 z^5 + 3857895 z^6 - 647700 z^7 + 53040 z^8) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

Standard Form

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MathML Form

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</annotation-xml> </semantics> </math>

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]