Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8369)

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`=5/2

http://functions.wolfram.com/07.22.03.8369.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 15/4}, -z] == ((2 Sqrt[z] (-1604888276866875 - 29346528491280000 z + 660535561592524800 z^2 + 611374975355289600 z^3 + 117241068286771200 z^4 + 7253411946823680 z^5 + 169666643230720 z^6 + 1522565906432 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (-4814664830600625 - 80702953351020000 z + 412713385513228800 z^2 + 548531921529446400 z^3 + 112975630722662400 z^4 + 7149877765079040 z^5 + 168722253742080 z^6 + 1519881551872 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (4814664830600625 - 80004708362779200 z + 542836567476403200 z^2 + 584612714339942400 z^3 + 115491268627660800 z^4 + 7211582132060160 z^5 + 169287679475712 z^6 + 1521492164608 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(986840141414400000 Sqrt[2] z^(9/4))

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]