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

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=41/8, b>=a

For fixed z and a=41/8, b=45/8

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

Input Form

Hypergeometric2F1[41/8, 45/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (-2 (-2845744 + 59265712 z - 619746633 z^2 + 4461908440 z^3 - 26260114636 z^4 + 151952736936 z^5 + 39674913513690 z^6 + 91667892661800 z^7 + 55109123872452 z^8 + 9457738171176 z^9 + 331477188135 z^10) + (1/Sqrt[1 - z]) (5691488 - 121377168 z + 1298047542 z^2 - 9529102803 z^3 + 56834386944 z^4 - 329123105220 z^5 + 84734125939372 z^6 + 229201012936350 z^7 + 168308313861168 z^8 + 39213474581676 z^9 + 2460397414158 z^10 + 18608356701 z^11)))/ (11382976 2^(3/4) (-1 + z)^16)

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]