Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9487)

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=-23/4, b>=a

For fixed z and a=-23/4, b=1/4

http://functions.wolfram.com/07.23.03.9487.01

Input Form

Hypergeometric2F1[-(23/4), 1/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (-47104 - 574816 z - 3346293 z^2 - 12875929 z^3 - 42935158 z^4 + 54940494 z^5 + 23552431 z^6 + 9241723 z^7 + 2664204 z^8 + 483328 z^9 + 40960 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-47104 - 621920 z - 3921109 z^2 - 16222222 z^3 - 55811087 z^4 + 12005336 z^5 + 78492925 z^6 + 32794154 z^7 + 11905927 z^8 + 3147532 z^9 + 524288 z^10 + 40960 z^11) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-47104 - 610144 z - 3774093 z^2 - 15346750 z^3 - 52374427 z^4 - 178247076 z^5 + 6460909 z^6 + 2482978 z^7 + 698715 z^8 + 123712 z^9 + 10240 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-47104 - 574816 z - 3346293 z^2 - 12875929 z^3 - 42935158 z^4 + 54940494 z^5 + 23552431 z^6 + 9241723 z^7 + 2664204 z^8 + 483328 z^9 + 40960 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1653098482035 Pi z^5 Sqrt[1 + Sqrt[1 + z]])

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]