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

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`=-11/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(11/2), -(23/4)}, -z] == (Sqrt[2] ((54539657778375 + 100887588301500 z + 21078128610000 z^2 - 20760587971200 z^3 + 5371579825920 z^4 - 923046727680 z^5 + 257511260160 z^6 - 1634992128000 z^7 + 129302003712 z^8 - 268435456 z^9) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (18179885926125 + 9389348199000 z - 10110201948000 z^2 + 3056176569600 z^3 - 571949199360 z^4 + 89243320320 z^5 + 25433210880 z^6 - 106283663360 z^7 + 1610612736 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (54539657778375 - 44551499107500 z + 15220051308000 z^2 - 3168106603200 z^3 + 554353873920 z^4 - 131139993600 z^5 + 190749081600 z^6 - 28751953920 z^7 + 67108864 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(54539657778375 z^(1/4))

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]