Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9451)

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/07.23.03.9451.01

Input Form

Hypergeometric2F1[-(23/4), -(1/4), 6, -z] == (1/(1096004293589205 Pi z^5)) (16384 (1 + z)^(1/4) (-2 (9844736 + 137057184 z + 934264485 z^2 + 4380359522 z^3 + 19057279395 z^4 - 158378608752 z^5 + 4283582667 z^6 + 1224686970 z^7 + 287229501 z^8 + 44646420 z^9 + 3341520 z^10) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (9844736 + 137057184 z + 934264485 z^2 + 4380359522 z^3 + 19057279395 z^4 - 158378608752 z^5 + 4283582667 z^6 + 1224686970 z^7 + 287229501 z^8 + 44646420 z^9 + 3341520 z^10) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-9844736 - 129673632 z - 838162941 z^2 - 3766500815 z^3 - 16325148840 z^4 + 36425547522 z^5 + 7048096419 z^6 + 2071569357 z^7 + 511749810 z^8 + 84280560 z^9 + 6683040 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> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn 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]