Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7160)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-17/4

http://functions.wolfram.com/07.22.03.7160.01

Input Form

HypergeometricPFQ[{4}, {-(17/4), 17/4}, z] == (1/(835584 z^(13/4))) ((-8 E^(2 Sqrt[z]) z^(1/4) (91216125 + 40540500 z + 8814960 z^2 + 1285248 z^3 + 152832 z^4 + 4096 z^5) - E^(4 Sqrt[z]) Sqrt[2 Pi] (-91216125 + 182432250 Sqrt[z] - 186486300 z + 129729600 z^(3/2) - 69355440 z^2 + 30602880 z^(5/2) - 11975040 z^3 + 4561920 z^(7/2) - 1731840 z^4 + 574464 z^(9/2) - 135168 z^5 + 16384 z^(11/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (91216125 + 182432250 Sqrt[z] + 186486300 z + 129729600 z^(3/2) + 69355440 z^2 + 30602880 z^(5/2) + 11975040 z^3 + 4561920 z^(7/2) + 1731840 z^4 + 574464 z^(9/2) + 135168 z^5 + 16384 z^(11/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 91216125 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]