Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8992)

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/07.22.03.8992.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 15/4}, z] == (-4 z^(1/4) (1063805671266975 + 5833243032844500 Sqrt[z] + 807414461577360 z + 15012209776374720 z^(3/2) + 13283392884652800 z^2 - 62880477326392320 z^(5/2) - 4102695605514240 z^3 + 17289428826636288 z^(7/2) + 319982439038976 z^4 - 1305134860861440 z^(9/2) - 8692146634752 z^5 + 35027190546432 z^(11/2) + 87124082688 z^6 - 349301637120 z^(13/2) - 268435456 z^7 + 1073741824 z^(15/2) + E^(4 Sqrt[z]) (-1063805671266975 + 5833243032844500 Sqrt[z] - 807414461577360 z + 15012209776374720 z^(3/2) - 13283392884652800 z^2 - 62880477326392320 z^(5/2) + 4102695605514240 z^3 + 17289428826636288 z^(7/2) - 319982439038976 z^4 - 1305134860861440 z^(9/2) + 8692146634752 z^5 + 35027190546432 z^(11/2) - 87124082688 z^6 - 349301637120 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (5558447535465825 + 33880061168553600 z + 90346829782809600 z^2 - 262827141186355200 z^3 + 70087237649694720 z^4 - 5246296151556096 z^5 + 140369127800832 z^6 - 1398011854848 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (5558447535465825 + 33880061168553600 z + 90346829782809600 z^2 - 262827141186355200 z^3 + 70087237649694720 z^4 - 5246296151556096 z^5 + 140369127800832 z^6 - 1398011854848 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(989708512521093120 z^(11/4))

Standard Form

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MathML Form

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</apply> <apply> <times /> <cn type='integer'> 70087237649694720 </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'> 262827141186355200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 90346829782809600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 33880061168553600 </cn> <ci> z </ci> </apply> <cn type='integer'> 5558447535465825 </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> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> 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</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]