Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7674)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-23/4

http://functions.wolfram.com/07.22.03.7674.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), 15/4}, z] == (1/(12887654400 z^(11/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (-10854718875 - 5472967500 z - 1162789200 z^2 + 370938240 z^3 + 51344640 z^4 - 3039232 z^5 + 65536 z^6) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-32564156625 + 65128313250 Sqrt[z] - 72243171000 z + 57648591000 z^(3/2) - 38626988400 z^2 + 23545922400 z^(5/2) - 10118908800 z^3 + 518918400 z^(7/2) + 2500243200 z^4 - 1600335360 z^(9/2) + 414935040 z^5 - 3194880 z^(11/2) - 23592960 z^6 + 3276800 z^(13/2) + 524288 z^7) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (32564156625 + 65128313250 Sqrt[z] + 72243171000 z + 57648591000 z^(3/2) + 38626988400 z^2 + 23545922400 z^(5/2) + 10118908800 z^3 + 518918400 z^(7/2) - 2500243200 z^4 - 1600335360 z^(9/2) - 414935040 z^5 - 3194880 z^(11/2) + 23592960 z^6 + 3276800 z^(13/2) - 524288 z^7) 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='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 57648591000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 72243171000 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 65128313250 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 32564156625 </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]