Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8640)

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`=-7/2

http://functions.wolfram.com/07.22.03.8640.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(7/2), -(1/4)}, z] == (1/3870720) ((4 (483840 + 967680 Sqrt[z] - 1935360 z + 477855 z^(3/2) - 1255212 z^2 + 148176 z^(5/2) - 452928 z^3 + 60672 z^(7/2) - 254976 z^4 - 4096 z^(9/2) + 16384 z^5 + E^(4 Sqrt[z]) (483840 - 967680 Sqrt[z] - 1935360 z - 477855 z^(3/2) - 1255212 z^2 - 148176 z^(5/2) - 452928 z^3 - 60672 z^(7/2) - 254976 z^4 + 4096 z^(9/2) + 16384 z^5)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (-5638815 - 4455360 z - 1645056 z^2 - 1032192 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (5638815 + 4455360 z + 1645056 z^2 + 1032192 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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<power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1935360 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 967680 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 483840 </cn> </apply> </apply> <cn type='integer'> 483840 </cn> </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]