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

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`=-7/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(7/2), -(15/4)}, -z] == (1/(1260653625 z^(1/4))) (Sqrt[2] ((1260653625 + 2065070700 z + 118752480 z^2 - 486319680 z^3 + 844462080 z^4 - 10332241920 z^5 + 1269301248 z^6 - 4194304 z^7) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (420217875 + 128066400 z - 237893040 z^2 + 96687360 z^3 + 198696960 z^4 - 795279360 z^5 + 19922944 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (1260653625 - 1296672300 z + 695051280 z^2 - 384975360 z^3 + 993484800 z^4 - 273285120 z^5 + 1048576 z^6) 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]