Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af1q)

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.af1q.01

Input Form

HypergeometricPFQ[{17/4}, {-(11/2), 15/4}, z] == (1/(862617600 Sqrt[2] z^(9/4))) ((2 Sqrt[z] (34976316375 + 43606836000 z + 14141088000 z^2 + 2872197120 z^3 + 91422720 z^4 - 14680064 z^5) BesselI[-(1/4), Sqrt[z]]^2 + (-104928949125 - 290712240000 z - 127512403200 z^2 - 31150080000 z^3 - 3321692160 z^4 + 138412032 z^5 + 8388608 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 30 Sqrt[z] (-6995263275 - 4457587680 z - 1265322240 z^2 - 219463680 z^3 - 4653056 z^4 + 1048576 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]