Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.age5)

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`=-9/2

http://functions.wolfram.com/07.22.03.age5.01

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), -(19/4)}, -z] == (1/(4095863627625 z^(1/4))) (Sqrt[2] (9 (455095958625 + 787768443000 z + 90030679200 z^2 - 174958882560 z^3 + 65752135680 z^4 - 56089313280 z^5 + 644308008960 z^6 - 92895444992 z^7 + 671088640 z^8) BesselJ[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (4095863627625 + 1628764483500 z - 2401629199200 z^2 + 961713466560 z^3 - 243300879360 z^4 - 317120348160 z^5 + 1375870648320 z^6 - 49262100480 z^7 + 67108864 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 12 z (-1365287875875 + 1277462340000 z - 556000275600 z^2 + 180385793280 z^3 - 76044165120 z^4 + 181211627520 z^5 - 57718865920 z^6 + 486539264 z^7) 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]