Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8z9)

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

For fixed z and a₁=-11/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.a8z9.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(3/2), 19/4}, -z] == (1/(981467136 Sqrt[2] z^(13/4))) ((2 Sqrt[z] (-3714726015 + 2572970400 z + 366702336 z^2 + 491372544 z^3 - 262209536 z^4 + 77594624 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^ 2 - (-11144178045 + 24700515840 z + 1335350016 z^2 + 590413824 z^3 - 282525696 z^4 + 67108864 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (11144178045 - 926269344 z + 311351040 z^2 + 556351488 z^3 - 275054592 z^4 + 73400320 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^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]