Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb86)

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=-37/8, b>=a

For fixed z and a=-37/8, b=-33/8

http://functions.wolfram.com/07.23.03.bb86.01

Input Form

Hypergeometric2F1[-(37/8), -(33/8), 19/4, z] == (1/(974044431999 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-118030 + 2838085 z - 41181740 z^2 + 685105135 z^3 + 25454204238 z^4 + 78424129155 z^5 + 63657822144 z^6 + 14453346729 z^7 + 654939084 z^8) + (1/Sqrt[1 - z]) (472120 - 11588400 z + 170344115 z^2 - 2821394485 z^3 - 39588729473 z^4 - 44577060681 z^5 + 41026607097 z^6 + 39986990241 z^7 + 5731419741 z^8 + 82939725 z^9)))

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]