Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8703)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.8703.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(5/2), 13/4}, -z] == -(((2 Sqrt[z] (288735522075 - 1238431194000 z - 1008306351360 z^2 + 672092467200 z^3 - 165584240640 z^4 + 203663867904 z^5 + 18673041408 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 - 3 (481225870125 + 1377825649200 z - 2221835616000 z^2 + 1014646026240 z^3 - 317977067520 z^4 + 187721318400 z^5 + 18438160384 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (1443677610375 + 1053631378800 z - 1943349408000 z^2 + 946944552960 z^3 - 300760104960 z^4 + 189923328000 z^5 + 18471714816 z^6 + 268435456 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(1859803545600 Sqrt[2] z^(7/4)))

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]