Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9va)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.a9va.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(3/2), 21/4}, z] == (1/(412316860416 z^(17/4))) ((221 (-4 z^(1/4) (18602008425 + 24802677900 Sqrt[z] + 13869591120 z + 3374965440 z^(3/2) + 65640960 z^2 + 54835200 z^(5/2) + 38707200 z^3 - 116293632 z^(7/2) + 9240576 z^4 - 33816576 z^(9/2) + 1048576 z^5 - 4194304 z^(11/2) + E^(4 Sqrt[z]) (18602008425 - 24802677900 Sqrt[z] + 13869591120 z - 3374965440 z^(3/2) + 65640960 z^2 - 54835200 z^(5/2) + 38707200 z^3 + 116293632 z^(7/2) + 9240576 z^4 + 33816576 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (18602008425 - 5972551200 z + 1397088000 z^2 - 397393920 z^3 + 433520640 z^4 + 132120576 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (18602008425 - 5972551200 z + 1397088000 z^2 - 397393920 z^3 + 433520640 z^4 + 132120576 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 433520640 </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'> 397393920 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1397088000 </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'> 5972551200 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 18602008425 </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]