Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a88x)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a88x.01

Input Form

HypergeometricPFQ[{-(15/4)}, {7/2, -(17/4)}, -z] == ((4 z (47220482925 + 29503303200 z - 11320934400 z^2 + 1318625280 z^3 - 73400320 z^4 + 2097152 z^5) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (141661448775 + 19987506000 z - 6146380800 z^2 + 684011520 z^3 - 37355520 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (424984346325 - 20986881300 z + 132091344000 z^2 - 46732492800 z^3 + 5351178240 z^4 - 295698432 z^5 + 8388608 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (55385694000 Sqrt[2] z^(7/4))

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]