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

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{13/4}, {11/2, -(17/4)}, z] == -((1/(848640 Sqrt[2] z^(15/4))) (7 (-20 z (20700696555 + 5069558340 z + 455347008 z^2 + 17861632 z^3 + 245760 z^4) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (310510448325 + 135188222400 z + 18242197920 z^2 + 1050478080 z^3 + 25518080 z^4 + 131072 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (931531344975 + 582999209100 z + 122759627760 z^2 + 10264815360 z^3 + 384061440 z^4 + 5046272 z^5) BesselI[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]