Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa36)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aa36.01

Input Form

HypergeometricPFQ[{-(7/4)}, {9/2, 17/4}, z] == (1/(855638016 z^(7/2))) ((-4 (-77414400 + 42529725 Sqrt[z] - 108444420 z + 24635520 z^(3/2) - 72495360 z^2 + 16611840 z^(5/2) - 74618880 z^3 - 2949120 z^(7/2) + 11993088 z^4 + 65536 z^(9/2) - 262144 z^5 + E^(4 Sqrt[z]) (77414400 + 42529725 Sqrt[z] + 108444420 z + 24635520 z^(3/2) + 72495360 z^2 + 16611840 z^(5/2) + 74618880 z^3 - 2949120 z^(7/2) - 11993088 z^4 + 65536 z^(9/2) + 262144 z^5)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (197358525 + 350859600 z + 249500160 z^2 + 307077120 z^3 - 48168960 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (197358525 + 350859600 z + 249500160 z^2 + 307077120 z^3 - 48168960 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 307077120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 249500160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 350859600 </cn> <ci> z </ci> </apply> <cn type='integer'> 197358525 </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]