Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8816)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.8816.01

Input Form

HypergeometricPFQ[{-(21/4)}, {1/2, -(17/4)}, z] == (1/1309458150) ((654729075 + 654729075 E^(4 Sqrt[z]) - 137837700 Sqrt[z] + 137837700 E^(4 Sqrt[z]) Sqrt[z] + 32432400 z + 32432400 E^(4 Sqrt[z]) z - 8648640 z^(3/2) + 8648640 E^(4 Sqrt[z]) z^(3/2) + 2661120 z^2 + 2661120 E^(4 Sqrt[z]) z^2 - 967680 z^(5/2) + 967680 E^(4 Sqrt[z]) z^(5/2) + 430080 z^3 + 430080 E^(4 Sqrt[z]) z^3 - 245760 z^(7/2) + 245760 E^(4 Sqrt[z]) z^(7/2) + 196608 z^4 + 196608 E^(4 Sqrt[z]) z^4 - 262144 z^(9/2) + 262144 E^(4 Sqrt[z]) z^(9/2) + 1048576 z^5 + 1048576 E^(4 Sqrt[z]) z^5 + 1048576 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) Erf[Sqrt[2] z^(1/4)] - 1048576 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) 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]