Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8603)

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/07.22.03.8603.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), 9/4}, -z] == ((2 Sqrt[z] (355208969115 + 277729452000 z - 130599786240 z^2 + 21493334016 z^3 - 1991442432 z^4 + 132120576 z^5 - 16777216 z^6) BesselJ[1/4, Sqrt[z]]^2 + 3 (105411381075 - 470581151040 z + 154418584320 z^2 - 23540858880 z^3 + 2131820544 z^4 - 146800640 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 2 Sqrt[z] (316234143225 - 412553100960 z + 149483093760 z^2 - 23167549440 z^3 + 2107047936 z^4 - 144703488 z^5 + 16777216 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(418455797760 Sqrt[2] z^(3/4))

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]