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

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=-39/8, b>=a

For fixed z and a=-39/8, b=29/8

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

Input Form

Hypergeometric2F1[-(39/8), 29/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-23363584 + 71642240 z - 22909403 z^2 - 37497383 z^3 - 112272545 z^4 + 830530547 z^5 - 1485699600 z^6 + 1254574464 z^7 - 527087616 z^8 + 89210880 z^9) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-23363584 + 71642240 z - 22909403 z^2 - 37497383 z^3 - 112272545 z^4 + 830530547 z^5 - 1485699600 z^6 + 1254574464 z^7 - 527087616 z^8 + 89210880 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-23363584 + 71642240 z - 22909403 z^2 - 37497383 z^3 - 112272545 z^4 + 830530547 z^5 - 1485699600 z^6 + 1254574464 z^7 - 527087616 z^8 + 89210880 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-23363584 + 80403584 z - 47379563 z^2 - 34979780 z^3 - 98931602 z^4 - 1611191428 z^5 + 5735028453 z^6 - 8141951136 z^7 + 5990603520 z^8 - 2279337984 z^9 + 356843520 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (651943777019535 Pi (1 + Sqrt[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]