Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aak0)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.aak0.01

Input Form

HypergeometricPFQ[{-(5/4)}, {11/2, -(1/4)}, z] == (1/(4922368 z^(9/2))) ((3 (-34563375 + 34563375 E^(4 Sqrt[z]) - 69126750 Sqrt[z] - 69126750 E^(4 Sqrt[z]) Sqrt[z] - 57172500 z + 57172500 E^(4 Sqrt[z]) z - 22176000 z^(3/2) - 22176000 E^(4 Sqrt[z]) z^(3/2) - 2162160 z^2 + 2162160 E^(4 Sqrt[z]) z^2 + 665280 z^(5/2) + 665280 E^(4 Sqrt[z]) z^(5/2) - 241920 z^3 + 241920 E^(4 Sqrt[z]) z^3 + 107520 z^(7/2) + 107520 E^(4 Sqrt[z]) z^(7/2) - 61440 z^4 + 61440 E^(4 Sqrt[z]) z^4 + 49152 z^(9/2) + 49152 E^(4 Sqrt[z]) z^(9/2) - 65536 z^5 + 65536 E^(4 Sqrt[z]) z^5 + 262144 z^(11/2) + 262144 E^(4 Sqrt[z]) z^(11/2) + 262144 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) Erf[Sqrt[2] z^(1/4)] - 262144 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) 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]