Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8rs)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8rs.01

Input Form

HypergeometricPFQ[{-(13/4)}, {11/2, -(9/4)}, z] == (1/(61800330240 z^(9/2))) ((-2511271137375 + 2511271137375 E^(4 Sqrt[z]) - 5022542274750 Sqrt[z] - 5022542274750 E^(4 Sqrt[z]) Sqrt[z] - 4198739044500 z + 4198739044500 E^(4 Sqrt[z]) z - 1700755056000 z^(3/2) - 1700755056000 E^(4 Sqrt[z]) z^(3/2) - 219988969200 z^2 + 219988969200 E^(4 Sqrt[z]) z^2 + 41902660800 z^(5/2) + 41902660800 E^(4 Sqrt[z]) z^(5/2) - 8821612800 z^3 + 8821612800 E^(4 Sqrt[z]) z^3 + 2075673600 z^(7/2) + 2075673600 E^(4 Sqrt[z]) z^(7/2) - 553512960 z^4 + 553512960 E^(4 Sqrt[z]) z^4 + 170311680 z^(9/2) + 170311680 E^(4 Sqrt[z]) z^(9/2) - 61931520 z^5 + 61931520 E^(4 Sqrt[z]) z^5 + 27525120 z^(11/2) + 27525120 E^(4 Sqrt[z]) z^(11/2) - 15728640 z^6 + 15728640 E^(4 Sqrt[z]) z^6 + 12582912 z^(13/2) + 12582912 E^(4 Sqrt[z]) z^(13/2) - 16777216 z^7 + 16777216 E^(4 Sqrt[z]) z^7 + 67108864 z^(15/2) + 67108864 E^(4 Sqrt[z]) z^(15/2) + 67108864 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(31/4) Erf[Sqrt[2] z^(1/4)] - 67108864 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(31/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

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]