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

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=41/8

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

Input Form

Hypergeometric2F1[-(35/8), 41/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-13074432 - 8120448 z - 10036845 z^2 - 20592390 z^3 - 87003945 z^4 + 4124328972 z^5 - 12839529472 z^6 + 16044887040 z^7 - 9214033920 z^8 + 2027683840 z^9) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-13074432 - 3217536 z - 5651037 z^2 - 15283695 z^3 - 77344155 z^4 + 1384413927 z^5 - 3785206624 z^6 + 4397981952 z^7 - 2398556160 z^8 + 506920960 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-13074432 - 8120448 z - 10036845 z^2 - 20592390 z^3 - 87003945 z^4 + 4124328972 z^5 - 12839529472 z^6 + 16044887040 z^7 - 9214033920 z^8 + 2027683840 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-13074432 - 8120448 z - 10036845 z^2 - 20592390 z^3 - 87003945 z^4 + 4124328972 z^5 - 12839529472 z^6 + 16044887040 z^7 - 9214033920 z^8 + 2027683840 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (727666649411625 Pi (1 + Sqrt[1 - z])^(1/4) z^5)

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]