Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7tb)

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=21/4

http://functions.wolfram.com/07.23.03.a7tb.01

Input Form

Hypergeometric2F1[-(23/4), 21/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (9844736 - 12152096 z + 21395957 z^2 - 58054139 z^3 + 313709627 z^4 + 10046155723 z^5 + 37245419552 z^6 + 60791719936 z^7 + 51771342848 z^8 + 22624075776 z^9 + 4026531840 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (9844736 - 2307360 z + 9243861 z^2 - 36658182 z^3 + 255655488 z^4 + 10359865350 z^5 + 47291575275 z^6 + 98037139488 z^7 + 112563062784 z^8 + 74395418624 z^9 + 26650607616 z^10 + 4026531840 z^11) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (9844736 - 4768544 z + 11589677 z^2 - 40835465 z^3 + 268081583 z^4 + 3915644413 z^5 + 12303493688 z^6 + 18187296256 z^7 + 14403829760 z^8 + 5939134464 z^9 + 1006632960 z^10) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - Sqrt[1 + z] (9844736 - 12152096 z + 21395957 z^2 - 58054139 z^3 + 313709627 z^4 + 10046155723 z^5 + 37245419552 z^6 + 60791719936 z^7 + 51771342848 z^8 + 22624075776 z^9 + 4026531840 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (52190680647105 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]