Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8515)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8515.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 17/4}, -z] == (Sqrt[Pi] z^(5/4) (-103297258322013380625 + 183639570350246010000 z - 180814346191011456000 z^2 + 397082485752809472000 z^3 + 151269518382022656000 z^4 + 13830355966356357120 z^5 + 462457043807109120 z^6 + 6406331342782464 z^7 + 36451387441152 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-7562178670362624000 + 19753189201816772625 z - 17263635472846224000 z^2 + 18374146495689600000 z^3 + 8738599035058421760 z^4 + 838705274410106880 z^5 + 28536462366474240 z^6 + 398275739910144 z^7 + 2274185183232 z^8 + 4294967296 z^9) Cos[2 Sqrt[z]] + 4 (-945272333795328000 - 9182645528297472000 z + 14397648545098959525 z^2 - 13586645756891592000 z^3 + 23337193611207168000 z^4 + 9303177035056988160 z^5 + 859136405319843840 z^6 + 28829414565347328 z^7 + 399970305835008 z^8 + 2277406408704 z^9 + 4294967296 z^10) Sin[2 Sqrt[z]]))/ (333900335153361715200 z^(9/2))

Standard Form

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MathML Form

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</apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 333900335153361715200 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]