Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7814)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-9/4

http://functions.wolfram.com/07.22.03.7814.01

Input Form

HypergeometricPFQ[{6}, {-(9/4), 21/4}, z] == -((1/(503316480 z^(17/4))) ((221 (8 E^(2 Sqrt[z]) z^(1/4) (237161925 + 114511320 z + 27609120 z^2 + 4435200 z^3 + 952320 z^4 + 65536 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-237161925 + 474323850 Sqrt[z] - 493970400 z + 355509000 z^(3/2) - 199584000 z^2 + 93804480 z^(5/2) - 39029760 z^3 + 15143040 z^(7/2) - 6336000 z^4 + 3379200 z^(9/2) - 1622016 z^5 + 294912 z^(11/2) + 131072 z^6) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (-237161925 - 474323850 Sqrt[z] - 493970400 z - 355509000 z^(3/2) - 199584000 z^2 - 93804480 z^(5/2) - 39029760 z^3 - 15143040 z^(7/2) - 6336000 z^4 - 3379200 z^(9/2) - 1622016 z^5 - 294912 z^(11/2) + 131072 z^6) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])))

Standard Form

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MathML Form

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<ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 474323850 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -237161925 </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> </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]