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

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=-17/8

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

Input Form

Hypergeometric2F1[-(35/8), -(17/8), 5, z] == (1/(818981679926025 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-8 (262656 - 4478832 z + 42232041 z^2 - 370083330 z^3 - 18161880301 z^4 - 28444864028 z^5 - 7440506241 z^6 - 10685010 z^7 + 365925 z^8) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-65664 + 1071999 z - 9783765 z^2 - 8245626840 z^3 - 14663771066 z^4 - 4256224609 z^5 - 21150465 z^6 + 731850 z^7) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-65664 + 1108935 z - 10379358 z^2 + 5089539177 z^3 + 11115638656 z^4 + 5133417737 z^5 + 435158010 z^6 - 8855385 z^7 + 292740 z^8) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 (262656 - 4478832 z + 42232041 z^2 - 370083330 z^3 - 18161880301 z^4 - 28444864028 z^5 - 7440506241 z^6 - 10685010 z^7 + 365925 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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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]