Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7ay)

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=47/8

http://functions.wolfram.com/07.23.03.b7ay.01

Input Form

Hypergeometric2F1[-(45/8), 47/8, -(11/2), z] == (1/64249856) ((1/(1 - Sqrt[z])^(23/4)) (32124928 - 184718336 Sqrt[z] + 631729408 z - 1658266880 z^(3/2) + 3694937120 z^2 - 7348129516 z^(5/2) + 13448697977 z^3 - 23094121336 z^(7/2) + 37741143440 z^4 - 59283040960 z^(9/2) + 90337305344 z^5 - 134474948608 z^(11/2) + 198789054464 z^6 - 273475502080 z^(13/2) + 294554501120 z^7 - 210495864832 z^(15/2) + 85688582144 z^8 - 14902362112 z^(17/2)) + (1/(1 + Sqrt[z])^(23/4)) (32124928 + 184718336 Sqrt[z] + 631729408 z + 1658266880 z^(3/2) + 3694937120 z^2 + 7348129516 z^(5/2) + 13448697977 z^3 + 23094121336 z^(7/2) + 37741143440 z^4 + 59283040960 z^(9/2) + 90337305344 z^5 + 134474948608 z^(11/2) + 198789054464 z^6 + 273475502080 z^(13/2) + 294554501120 z^7 + 210495864832 z^(15/2) + 85688582144 z^8 + 14902362112 z^(17/2)))

Standard Form

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MathML Form

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</cn> </apply> </apply> <cn type='integer'> 32124928 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]