Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9097)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9097.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 23/4}, -z] == (Sqrt[Pi] (1251901346175290435625 - 4451204786401032660000 z + 4162165514556809760000 z^2 - 2306308163910266880000 z^3 + 1435036190877499392000 z^4 + 1450141834991999385600 z^5 + 168132386665739059200 z^6 + 6325968692890828800 z^7 + 94183156717977600 z^8 + 562812514467840 z^9 + 1099511627776 z^10) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-250222674513569428125 + 258137527635369018000 z - 141293618509051008000 z^2 + 76163951491142860800 z^3 + 88811834210323660800 z^4 + 10436468939056742400 z^5 + 394283587605626880 z^6 + 5879880021442560 z^7 + 35162897252352 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (83144900302042044375 + 141227808645765114000 z - 94653866027710080000 z^2 + 33132989912795136000 z^3 + 82065229514647142400 z^4 + 10158216822757785600 z^5 + 389982079879741440 z^6 + 5853723670609920 z^7 + 35111357644800 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]]))/(1733552594563262054400 z^(19/4))

Standard Form

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MathML Form

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<power /> <apply> <times /> <cn type='integer'> 1733552594563262054400 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 4 </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]