Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9589)

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`=9/2

http://functions.wolfram.com/07.22.03.9589.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, -(13/4)}, -z] == ((4 z (4485945877875 + 911430273600 z + 890363232000 z^2 - 426671308800 z^3 + 75211407360 z^4 - 8745123840 z^5 + 1325400064 z^6 + 67108864 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (13457837633625 + 170893176300 z + 680870836800 z^2 - 246655411200 z^3 + 41061335040 z^4 - 4730388480 z^5 + 641728512 z^6 + 33554432 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (40373512900875 - 7177513404600 z + 1545468724800 z^2 + 4180406630400 z^3 - 1800316108800 z^4 + 311167549440 z^5 - 36201037824 z^6 + 5234491392 z^7 + 268435456 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1781650728000 Sqrt[2] z^(11/4))

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]