Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4lc)

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=-45/8

http://functions.wolfram.com/07.23.03.b4lc.01

Input Form

Hypergeometric2F1[-(47/8), -(45/8), 5, z] == (65536 2^(1/4) (64 Sqrt[1 - z] (-1951074528 + 60747518377 z - 1149934873633 z^2 + 23055177015507 z^3 + 1047830352030091 z^4 + 4550810335435385 z^5 + 5880965777587005 z^6 + 2598195070833505 z^7 + 359005532790905 z^8 + 10230314520426 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 32 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-1951074528 + 60747518377 z - 1149934873633 z^2 + 23055177015507 z^3 + 1047830352030091 z^4 + 4550810335435385 z^5 + 5880965777587005 z^6 + 2598195070833505 z^7 + 359005532790905 z^8 + 10230314520426 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 32 Sqrt[1 - z] (-1951074528 + 60747518377 z - 1149934873633 z^2 + 23055177015507 z^3 + 1047830352030091 z^4 + 4550810335435385 z^5 + 5880965777587005 z^6 + 2598195070833505 z^7 + 359005532790905 z^8 + 10230314520426 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (62434384896 - 1982942078624 z + 38006464360501 z^2 - 760568035094504 z^3 + 35945369641854988 z^4 + 328338643807945960 z^5 + 740914806127015870 z^6 + 576319844886633640 z^7 + 158158520895257740 z^8 + 12911810107284088 z^9 + 167668600664565 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (2261598829974760090815 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]