Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8663)

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`=-7/2

http://functions.wolfram.com/07.22.03.8663.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(7/2), 21/4}, -z] == ((2 Sqrt[z] (-92905480235643075 - 117623922040825200 z - 15543540607795200 z^2 + 176729875660800 z^3 + 3624738530918400 z^4 - 885984596066304 z^5 + 109493077671936 z^6 - 9943923032064 z^7 + 2615635083264 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]]^2 - 3 (-154842467059405125 - 306150068865841200 z + 323823762662400 z^2 - 6436248698880000 z^3 + 4715303052902400 z^4 - 1008672555663360 z^5 + 121605892079616 z^6 - 12131135127552 z^7 + 2555505541120 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-464527401178215375 + 72541582582669200 z - 2775632251392000 z^2 - 4303509925478400 z^3 + 4463348288716800 z^4 - 984120589025280 z^5 + 119318620667904 z^6 - 11838003609600 z^7 + 2564095475712 z^8 + 68719476736 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(5566821197414400 Sqrt[2] z^(15/4))

Standard Form

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MathML Form

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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]