Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9ra)

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`=-9/2

http://functions.wolfram.com/07.22.03.a9ra.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(9/2), 21/4}, z] == (221 (-4 z^(1/4) (25949801752875 + 34599735670500 Sqrt[z] + 22204665529200 z + 8516858011200 z^(3/2) + 1974620229120 z^2 + 265687050240 z^(5/2) + 16592855040 z^3 - 16539156480 z^(7/2) + 464977920 z^4 - 1825308672 z^(9/2) + 11534336 z^5 - 46137344 z^(11/2) + E^(4 Sqrt[z]) (25949801752875 - 34599735670500 Sqrt[z] + 22204665529200 z - 8516858011200 z^(3/2) + 1974620229120 z^2 - 265687050240 z^(5/2) + 16592855040 z^3 + 16539156480 z^(7/2) + 464977920 z^4 + 1825308672 z^(9/2) + 11534336 z^5 + 46137344 z^(11/2))) + 11 E^(2 Sqrt[z]) Sqrt[2 Pi] (2359072886625 - 497738455200 z + 71360352000 z^2 - 11276697600 z^3 + 5883494400 z^4 + 660602880 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + 11 E^(2 Sqrt[z]) Sqrt[2 Pi] (2359072886625 - 497738455200 z + 71360352000 z^2 - 11276697600 z^3 + 5883494400 z^4 + 660602880 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (49478023249920 z^(17/4))

Standard Form

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MathML Form

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11276697600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 71360352000 </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'> 497738455200 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 2359072886625 </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> <times /> <cn type='integer'> 11 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 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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]