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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(11/2), 23/4}, z] == (19 (4 z^(1/4) (-26264240610733125 - 35018987480977500 Sqrt[z] - 28015189984782000 z - 16008679991304000 z^(3/2) - 7114968885024000 z^2 - 2587261412736000 z^(5/2) - 796080434688000 z^3 - 212288115916800 z^(7/2) - 49950144921600 z^4 - 10506641080320 z^(9/2) - 1984655523840 z^5 - 331370987520 z^(11/2) - 46254784512 z^6 - 4764729344 z^(13/2) - 268435456 z^7 + E^(4 Sqrt[z]) (26264240610733125 - 35018987480977500 Sqrt[z] + 28015189984782000 z - 16008679991304000 z^(3/2) + 7114968885024000 z^2 - 2587261412736000 z^(5/2) + 796080434688000 z^3 - 212288115916800 z^(7/2) + 49950144921600 z^4 - 10506641080320 z^(9/2) + 1984655523840 z^5 - 331370987520 z^(11/2) + 46254784512 z^6 - 4764729344 z^(13/2) + 268435456 z^7)) + 26264240610733125 E^(2 Sqrt[z]) Sqrt[2 Pi] Erf[Sqrt[2] z^(1/4)] - 26264240610733125 E^(2 Sqrt[z]) Sqrt[2 Pi] Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z])/(1395193282560 z^(19/4))

Standard Form

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MathML Form

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<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 </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]