Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ada6)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.ada6.01

Input Form

HypergeometricPFQ[{9/4}, {-(9/2), -(17/4)}, z] == (1/(46990125 Sqrt[2])) (z^(1/4) ((46990125 + 99508500 z + 68234400 z^2 + 18158400 z^3 + 3456000 z^4 + 2211840 z^5 + 262144 z^6) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-46990125 - 61916400 z - 22042800 z^2 - 4515840 z^3 - 921600 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (46990125 + 24324300 z + 5924880 z^2 + 1094400 z^3 + 307200 z^4 + 65536 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]