Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9049)

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`=9/2

http://functions.wolfram.com/07.22.03.9049.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 23/4}, -z] == (Sqrt[Pi] (-32100034517315139375 - 342400368184694820000 z + 747055348766606880000 z^2 - 650497174436229120000 z^3 + 551936996491345920000 z^4 + 706479355508922777600 z^5 + 99154997264410214400 z^6 + 4379516787385958400 z^7 + 74863534827110400 z^8 + 505088154009600 z^9 + 1099511627776 z^10) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-10700011505771713125 + 43334691652768698000 z - 38656155156877440000 z^2 + 28190469507405004800 z^3 + 43094313982063411200 z^4 + 6147705986718105600 z^5 + 272855265580154880 z^6 + 4673080110612480 z^7 + 31555124723712 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (32100034517315139375 + 3006903599977914000 z - 18596560405917312000 z^2 + 9025272081745920000 z^3 + 39216836903937638400 z^4 + 5956841643127603200 z^5 + 269447527126794240 z^6 + 4649629589176320 z^7 + 31503585116160 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]]))/(800101197490736332800 z^(19/4))

Standard Form

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MathML Form

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800101197490736332800 </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]