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

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=3/8, b>=a

For fixed z and a=3/8, b=45/8

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

Input Form

Hypergeometric2F1[3/8, 45/8, -(11/2), z] == -((1/(338415616 (1 - z)^(23/2))) (Sqrt[1 - z] (-338415616 + 3947541248 z - 21228128992 z^2 + 70025652807 z^3 - 160177604169 z^4 + 280157282724 z^5 - 503905644242 z^6 + 137045814847 z^7 - 53039166629 z^8 + 15358560454 z^9 - 2795085488 z^10 + 236989792 z^11) Cos[(3 ArcSin[Sqrt[z]])/4] + 2 Sqrt[z] (-126905856 + 1498835072 z - 8164862594 z^2 + 27293859153 z^3 - 63260491888 z^4 + 111874180759 z^5 - 283327931514 z^6 + 80905506767 z^7 - 30191936516 z^8 + 8363239737 z^9 - 1456790192 z^10 + 118494896 z^11) Sin[(3 ArcSin[Sqrt[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]