Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4yy)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-5/8

http://functions.wolfram.com/07.23.03.b4yy.01

Input Form

Hypergeometric2F1[-(47/8), -(5/8), 5, z] == (65536 2^(1/4) (2 Sqrt[1 - z] (-102945792 + 1510943968 z - 11791079927 z^2 + 80581656463 z^3 + 570183059726 z^4 + 80276861966 z^5 - 20559327019 z^6 + 4722559491 z^7 - 742031004 z^8 + 56911920 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-102945792 + 1510943968 z - 11791079927 z^2 + 80581656463 z^3 + 570183059726 z^4 + 80276861966 z^5 - 20559327019 z^6 + 4722559491 z^7 - 742031004 z^8 + 56911920 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-102945792 + 1510943968 z - 11791079927 z^2 + 80581656463 z^3 + 570183059726 z^4 + 80276861966 z^5 - 20559327019 z^6 + 4722559491 z^7 - 742031004 z^8 + 56911920 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 (-51472896 + 787642544 z - 6362431971 z^2 + 43900549374 z^3 - 709890273337 z^4 - 809042047212 z^5 + 91046637003 z^6 - 23069107282 z^7 + 5123704833 z^8 - 773332560 z^9 + 56911920 z^10) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (63594152067451005 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)

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]