Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8608)

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`=-9/2

http://functions.wolfram.com/07.22.03.8608.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), 15/4}, z] == (11 (4 z^(1/4) (-664057163030625 - 885409550707500 Sqrt[z] - 289611793926000 z + 153529143768000 z^(3/2) - 45903663187200 z^2 + 127164517401600 z^(5/2) - 8152119521280 z^3 + 28746511073280 z^(7/2) - 834857533440 z^4 + 3112513044480 z^(9/2) - 56041144320 z^5 + 212185645056 z^(11/2) - 3070230528 z^6 + 11475615744 z^(13/2) - 268435456 z^7 + 1073741824 z^(15/2) + E^(4 Sqrt[z]) (664057163030625 - 885409550707500 Sqrt[z] + 289611793926000 z + 153529143768000 z^(3/2) + 45903663187200 z^2 + 127164517401600 z^(5/2) + 8152119521280 z^3 + 28746511073280 z^(7/2) + 834857533440 z^4 + 3112513044480 z^(9/2) + 56041144320 z^5 + 212185645056 z^(11/2) + 3070230528 z^6 + 11475615744 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (664057163030625 - 418715846640000 z + 312641165491200 z^2 + 476405585510400 z^3 + 112095431884800 z^4 + 12263431864320 z^5 + 838525255680 z^6 + 45097156608 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (664057163030625 - 418715846640000 z + 312641165491200 z^2 + 476405585510400 z^3 + 112095431884800 z^4 + 12263431864320 z^5 + 838525255680 z^6 + 45097156608 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(31171154647449600 z^(11/4))

Standard Form

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MathML Form

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type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 212185645056 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 56041144320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3112513044480 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 834857533440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 28746511073280 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8152119521280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 127164517401600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 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type='integer'> 45097156608 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 838525255680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12263431864320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 112095431884800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 476405585510400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 312641165491200 </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'> 418715846640000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 664057163030625 </cn> </apply> <apply> <ci> Erfi 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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]