Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8125)

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/07.22.03.8125.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 11/4}, -z] == -(((2 Sqrt[z] (677644592625 - 3449950218000 z + 4080053203200 z^2 - 1947035750400 z^3 + 937510502400 z^4 + 506635223040 z^5 + 26088570880 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - (2032933777875 - 637783146000 z + 4129181971200 z^2 - 1943585280000 z^3 + 661561344000 z^4 + 490780753920 z^5 + 25920798720 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-2032933777875 - 3699142246800 z + 4398278227200 z^2 - 2026529280000 z^3 + 820548403200 z^4 + 500217937920 z^5 + 26021462016 z^6 + 268435456 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(8539914240000 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]