Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agop)

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.agop.01

Input Form

HypergeometricPFQ[{23/4}, {7/2, -(23/4)}, -z] == ((-8 z (10167942015 - 14136277680 z - 1117831680 z^2 + 715825152 z^3 + 37945344 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (-134908648875 + 103985516880 z - 11548454400 z^2 - 9901301760 z^3 + 63504384 z^4 + 26214400 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-674543244375 + 446970069000 z - 110347332480 z^2 - 42718556160 z^3 + 5628887040 z^4 + 375914496 z^5 + 8388608 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (13291691490 Sqrt[2] z^(5/4))

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]