Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bd1d)

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=-35/8, b>=a

For fixed z and a=-35/8, b=25/8

http://functions.wolfram.com/07.23.03.bd1d.01

Input Form

Hypergeometric2F1[-(35/8), 25/8, 17/4, z] == (8 2^(1/4) (112860 - 40755 z - 110979 z^2 + 2120399 z^3 - 5277589 z^4 + 5681568 z^5 - 2914560 z^6 + 585728 z^7 + (1/Sqrt[1 - z]) (-112860 + 97185 z + 104709 z^2 + 5197715 z^3 - 21534701 z^4 + 35870992 z^5 - 30549120 z^6 + 13268992 z^7 - 2342912 z^8)))/ (58973153 (1 + Sqrt[1 - z])^(1/4) z^3)

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]