Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9715)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.9715.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(11/2), 17/4}, -z] == ((2 Sqrt[z] (-794063933637975 - 1008335153826000 z - 32334931157760 z^2 + 77681924812800 z^3 - 11145482403840 z^4 + 648155234304 z^5 - 19075694592 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 + 3 (1323439889396625 + 2621671399947600 z + 34695403142400 z^2 - 88535547555840 z^3 + 11742543544320 z^4 - 665242828800 z^5 + 19310575616 z^6 - 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-3970319668189875 + 605001092295600 z - 104086209427200 z^2 + 86743045877760 z^3 - 11651185704960 z^4 + 662726246400 z^5 - 19277021184 z^6 + 268435456 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (120858618101760 Sqrt[2] z^(11/4))

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]