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

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=1/4, b_1`>=-11/2

For fixed z and a₁=1/4, b_1`=-3/2

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

Input Form

HypergeometricPFQ[{1/4}, {-(3/2), 21/4}, z] == (1/(4294967296 z^(17/4))) ((3315 (-4 z^(1/4) (295269975 + 393693300 Sqrt[z] + 251753040 z + 95705280 z^(3/2) + 21443840 z^2 + 2391040 z^(5/2) + 28672 z^3 - 114688 z^(7/2) + E^(4 Sqrt[z]) (295269975 - 393693300 Sqrt[z] + 251753040 z - 95705280 z^(3/2) + 21443840 z^2 - 2391040 z^(5/2) + 28672 z^3 + 114688 z^(7/2))) + 7 E^(2 Sqrt[z]) Sqrt[2 Pi] (42181425 - 9028800 z + 1267200 z^2 - 180224 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + 7 E^(2 Sqrt[z]) Sqrt[2 Pi] (42181425 - 9028800 z + 1267200 z^2 - 180224 z^3 + 65536 z^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]