Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7716)

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=-19/4

http://functions.wolfram.com/07.22.03.7716.01

Input Form

HypergeometricPFQ[{6}, {-(19/4), 11/4}, z] == (1/(1540915200 z^(7/4))) ((-16 E^(2 Sqrt[z]) z^(3/4) (79053975 - 4801500 z - 64769760 z^2 + 2835264 z^3 + 354304 z^4 + 16384 z^5) - E^(4 Sqrt[z]) Sqrt[2 Pi] (237161925 - 474323850 Sqrt[z] + 681080400 z - 729729000 z^(3/2) + 176904000 z^2 + 450515520 z^(5/2) - 484323840 z^3 + 172748160 z^(7/2) + 15475200 z^4 - 27955200 z^(9/2) + 3293184 z^5 + 1933312 z^(11/2) + 131072 z^6) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (237161925 + 474323850 Sqrt[z] + 681080400 z + 729729000 z^(3/2) + 176904000 z^2 - 450515520 z^(5/2) - 484323840 z^3 - 172748160 z^(7/2) + 15475200 z^4 + 27955200 z^(9/2) + 3293184 z^5 - 1933312 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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<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]