Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7428)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-19/4

http://functions.wolfram.com/07.22.03.7428.01

Input Form

HypergeometricPFQ[{5}, {-(19/4), 15/4}, z] == (1/(56033280 z^(11/4))) ((-16 E^(2 Sqrt[z]) z^(3/4) (70945875 + 32432400 z + 6606720 z^2 - 1413120 z^3 - 198144 z^4 + 8192 z^5) - E^(4 Sqrt[z]) Sqrt[2 Pi] (212837625 - 425675250 Sqrt[z] + 462161700 z - 356756400 z^(3/2) + 227026800 z^2 - 129729600 z^(5/2) + 55036800 z^3 - 6289920 z^(7/2) - 9434880 z^4 + 6389760 z^(9/2) - 1597440 z^5 + 65536 z^6) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (212837625 + 425675250 Sqrt[z] + 462161700 z + 356756400 z^(3/2) + 227026800 z^2 + 129729600 z^(5/2) + 55036800 z^3 + 6289920 z^(7/2) - 9434880 z^4 - 6389760 z^(9/2) - 1597440 z^5 + 65536 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</apply> <apply> <times /> <cn type='integer'> 356756400 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 462161700 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 425675250 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 212837625 </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]