Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c8aj)

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=21/8, b>=a

For fixed z and a=21/8, b=41/8

http://functions.wolfram.com/07.23.03.c8aj.01

Input Form

Hypergeometric2F1[21/8, 41/8, -(23/4), z] == (7691200 (1 + Sqrt[1 - z]) - 83600 (1463 + 1417 Sqrt[1 - z]) z + 2200 (427901 + 401415 Sqrt[1 - z]) z^2 - 495 (9601513 + 8738423 Sqrt[1 - z]) z^3 + 5 (3669719089 + 3257824298 Sqrt[1 - z]) z^4 - 65 (971802587 + 854038767 Sqrt[1 - z]) z^5 + 715 (387827363 + 351521000 Sqrt[1 - z]) z^6 + 3 (965583560537 + 271097098963 Sqrt[1 - z]) z^7 + 3 (622707800645 + 86696840574 Sqrt[1 - z]) z^8 + 377863317 (379 + 3 Sqrt[1 - z]) z^9 - 9688803 (479 + 4 Sqrt[1 - z]) z^10 + 155020848 z^11)/(7691200 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (1 - z)^(27/2))

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]