Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8659)

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/07.22.03.8659.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(7/2), 17/4}, -z] == ((2 Sqrt[z] (-230534690411025 - 333943255245600 z + 36699266419200 z^2 + 101930263142400 z^3 - 31453284925440 z^4 + 4622502592512 z^5 - 479861932032 z^6 + 146565758976 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]]^2 - 3 (-384224484018375 - 829798391822400 z - 183030822374400 z^2 + 143737097011200 z^3 - 36858131251200 z^4 + 5230653603840 z^5 - 601765183488 z^6 + 142807662592 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-1152673452055125 - 30358477749600 z - 109617360652800 z^2 + 133381798502400 z^3 - 35730771148800 z^4 + 5113726894080 z^5 - 585558392832 z^6 + 143344533504 z^7 + 4294967296 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(155651250585600 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]