Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7450)

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=-17/4

http://functions.wolfram.com/07.22.03.7450.01

Input Form

HypergeometricPFQ[{5}, {-(17/4), 17/4}, z] == (1/(13369344 z^(13/4))) ((24 E^(2 Sqrt[z]) z^(1/4) (-91216125 - 45945900 z - 12141360 z^2 - 2862976 z^3 - 441600 z^4 + 12288 z^5) - E^(4 Sqrt[z]) Sqrt[2 Pi] (-273648375 + 547296750 Sqrt[z] - 575675100 z + 421621200 z^(3/2) - 243991440 z^2 + 120415680 z^(5/2) - 57214080 z^3 + 29652480 z^(7/2) - 14657280 z^4 + 5136384 z^(9/2) - 811008 z^5 - 131072 z^(11/2) + 65536 z^6) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (273648375 + 547296750 Sqrt[z] + 575675100 z + 421621200 z^(3/2) + 243991440 z^2 + 120415680 z^(5/2) + 57214080 z^3 + 29652480 z^(7/2) + 14657280 z^4 + 5136384 z^(9/2) + 811008 z^5 - 131072 z^(11/2) - 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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<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]