Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8nx)

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=-21/4, b>=a

For fixed z and a=-21/4, b=9/4

http://functions.wolfram.com/07.23.03.a8nx.01

Input Form

Hypergeometric2F1[-(21/4), 9/4, 6, -z] == (1/(1852856480475 Pi z^5)) (16384 (1 + z)^(1/4) (2 (-4073472 - 27941472 z - 72479823 z^2 - 67999932 z^3 + 45026982 z^4 + 469443172 z^5 + 795590961 z^6 + 704768064 z^7 + 363006336 z^8 + 103428864 z^9 + 12684672 z^10) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-4073472 - 24886368 z - 54292407 z^2 - 30017988 z^3 + 62180118 z^4 + 194992996 z^5 + 225878169 z^6 + 139647816 z^7 + 45900624 z^8 + 6342336 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-4073472 - 27941472 z - 72479823 z^2 - 67999932 z^3 + 45026982 z^4 + 469443172 z^5 + 795590961 z^6 + 704768064 z^7 + 363006336 z^8 + 103428864 z^9 + 12684672 z^10) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))

Standard Form

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MathML Form

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type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </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]