Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9bc)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a9bc.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(9/2), 23/4}, z] == (209 (4 z^(1/4) (-640591234408125 - 854121645877500 Sqrt[z] - 554024851380000 z - 218092322448000 z^(3/2) - 52739076499200 z^2 - 7101130982400 z^(5/2) - 384723763200 z^3 + 131604480000 z^(7/2) - 14553907200 z^4 + 55419076608 z^(9/2) - 874512384 z^5 + 3447717888 z^(11/2) - 16777216 z^6 + 67108864 z^(13/2) + E^(4 Sqrt[z]) (640591234408125 - 854121645877500 Sqrt[z] + 554024851380000 z - 218092322448000 z^(3/2) + 52739076499200 z^2 - 7101130982400 z^(5/2) + 384723763200 z^3 + 131604480000 z^(7/2) + 14553907200 z^4 + 55419076608 z^(9/2) + 874512384 z^5 + 3447717888 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (640591234408125 - 129272465322000 z + 17093879712000 z^2 - 2245501440000 z^3 + 479040307200 z^4 + 218989854720 z^5 + 13740539904 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (640591234408125 - 129272465322000 z + 17093879712000 z^2 - 2245501440000 z^3 + 479040307200 z^4 + 218989854720 z^5 + 13740539904 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (369435906932736 z^(19/4))

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,a₂},{b₁},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]