Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7sy)

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`=7/2

http://functions.wolfram.com/07.22.03.a7sy.01

Input Form

HypergeometricPFQ[{-(17/4)}, {7/2, -(15/4)}, z] == ((-8 z (-1606603005 + 6364252944 z + 1732642560 z^2 + 200577024 z^3 + 14352384 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (10384817625 + 8345892240 z + 1936210176 z^2 + 214683648 z^3 + 15269888 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-155772264375 + 49847124600 z + 63437904000 z^2 + 15202916352 z^3 + 1698988032 z^4 + 121110528 z^5 + 8388608 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (18888193170 Sqrt[2] z^(5/4))

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]