Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9305)

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=-7/4

http://functions.wolfram.com/07.23.03.9305.01

Input Form

Hypergeometric2F1[-(23/4), -(7/4), 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (-2048 - 36000 z - 327123 z^2 - 2224654 z^3 - 16255449 z^4 + 173717532 z^5 - 143551445 z^6 + 8583138 z^7 + 785889 z^8 + 69264 z^9 + 3456 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-2048 - 38048 z - 363123 z^2 - 2551777 z^3 - 18480103 z^4 + 157462083 z^5 + 30166087 z^6 - 134968307 z^7 + 9369027 z^8 + 855153 z^9 + 72720 z^10 + 3456 z^11) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-2048 - 37536 z - 353979 z^2 - 2467531 z^3 - 17902059 z^4 - 97777251 z^5 + 406717111 z^6 - 189986121 z^7 + 201231 z^8 + 17559 z^9 + 864 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-2048 - 36000 z - 327123 z^2 - 2224654 z^3 - 16255449 z^4 + 173717532 z^5 - 143551445 z^6 + 8583138 z^7 + 785889 z^8 + 69264 z^9 + 3456 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (2125412334045 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]