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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=1/2

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

Input Form

HypergeometricPFQ[{19/4}, {1/2, -(23/4)}, -z] == (1/(5246720325 z^(1/4))) (Sqrt[2] ((5246720325 + 19161935100 z + 24332616000 z^2 + 6631446528 z^3 - 708083712 z^4 - 181665792 z^5 + 4194304 z^6) BesselJ[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-1748906775 - 4055436000 z - 44029440 z^2 + 955121664 z^3 + 133496832 z^4 + 10485760 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 4 z (-5246720325 + 3137173200 z + 3663797760 z^2 + 137797632 z^3 - 22609920 z^4 + 1048576 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]