Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6nu)

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=-45/8, b>=a

For fixed z and a=-45/8, b=7/8

http://functions.wolfram.com/07.23.03.b6nu.01

Input Form

Hypergeometric2F1[-(45/8), 7/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-457080832 + 4972539520 z - 24731507255 z^2 + 74899643715 z^3 - 159270379450 z^4 - 37366719610 z^5 + 27026993125 z^6 - 13976319225 z^7 + 4839354300 z^8 - 1005312000 z^9 + 94786560 z^10) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-457080832 + 4972539520 z - 24731507255 z^2 + 74899643715 z^3 - 159270379450 z^4 - 37366719610 z^5 + 27026993125 z^6 - 13976319225 z^7 + 4839354300 z^8 - 1005312000 z^9 + 94786560 z^10) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-457080832 + 4972539520 z - 24731507255 z^2 + 74899643715 z^3 - 159270379450 z^4 - 37366719610 z^5 + 27026993125 z^6 - 13976319225 z^7 + 4839354300 z^8 - 1005312000 z^9 + 94786560 z^10) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-457080832 + 5143944832 z - 26549340935 z^2 + 83688978360 z^3 - 185076378175 z^4 + 233783009240 z^5 - 196216499765 z^6 + 133036213200 z^7 - 64773017925 z^8 + 21243948000 z^9 - 4202922240 z^10 + 379146240 z^11) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (57126864281411925 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^5)

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]