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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-9/4, b>=a

For fixed z and a=-9/4, b=23/4

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

Input Form

Hypergeometric2F1[-(9/4), 23/4, 6, -z] == (16384 Sqrt[2] ((6144 - 8736 z + 15897 z^2 - 37875 z^3 + 148800 z^4 + 2561536 z^5 + 4161536 z^6 + 1835008 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (6144 - 8736 z + 15897 z^2 - 37875 z^3 + 148800 z^4 + 2561536 z^5 + 4161536 z^6 + 1835008 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (6144 - 10272 z + 19185 z^2 - 44325 z^3 + 163200 z^4 + 710656 z^5 + 458752 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (6144 - 8736 z + 15897 z^2 - 37875 z^3 + 148800 z^4 + 2561536 z^5 + 4161536 z^6 + 1835008 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (14767778025 Pi z^5 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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<cn type='integer'> -1 </cn> </apply> </apply> </apply> </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]