Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7s4)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a7s4.01

Input Form

HypergeometricPFQ[{-(17/4)}, {5/2, 3/4}, z] == (1/(1550545920 z^(3/2))) ((4 (1432080 + 2864160 Sqrt[z] - 19094400 z + 151810560 z^(3/2) + 44802495 z^2 - 202268076 z^(5/2) - 8911152 z^3 + 36792000 z^(7/2) + 396544 z^4 - 1598464 z^(9/2) - 4096 z^5 + 16384 z^(11/2) + E^(4 Sqrt[z]) (-1432080 + 2864160 Sqrt[z] + 19094400 z + 151810560 z^(3/2) - 44802495 z^2 - 202268076 z^(5/2) + 8911152 z^3 + 36792000 z^(7/2) - 396544 z^4 - 1598464 z^(9/2) + 4096 z^5 + 16384 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (717084225 - 834425280 z + 148342272 z^2 - 6406144 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (-717084225 + 834425280 z - 148342272 z^2 + 6406144 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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type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 65536 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6406144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 148342272 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 834425280 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 717084225 </cn> </apply> <apply> <ci> Erf </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> <power /> <ci> z </ci> <cn 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/> <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> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4096 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1598464 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 396544 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> 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type='integer'> 1432080 </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]