Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b75w)

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=-45/8, b>=a

For fixed z and a=-45/8, b=39/8

http://functions.wolfram.com/07.23.03.b75w.01

Input Form

Hypergeometric2F1[-(45/8), 39/8, -(7/2), z] == (1/2555392) ((1/(1 - Sqrt[z])^(11/4)) (1277696 - 3513664 Sqrt[z] + 13084976 z - 28297544 z^(3/2) + 78440695 z^2 - 155636492 z^(5/2) + 431804208 z^3 - 861349632 z^(7/2) + 3836921088 z^4 + 15935169536 z^(9/2) - 78354006016 z^5 + 59584937984 z^(11/2) + 84279230464 z^6 - 133189861376 z^(13/2) + 48432676864 z^7) + (1/(1 + Sqrt[z])^(11/4)) (1277696 + 3513664 Sqrt[z] + 13084976 z + 28297544 z^(3/2) + 78440695 z^2 + 155636492 z^(5/2) + 431804208 z^3 + 861349632 z^(7/2) + 3836921088 z^4 - 15935169536 z^(9/2) - 78354006016 z^5 - 59584937984 z^(11/2) + 84279230464 z^6 + 133189861376 z^(13/2) + 48432676864 z^7))

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]