Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7zc)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a7zc.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(9/2), 23/4}, z] == (19 (2 Sqrt[z] (-246627625247128125 - 221425265601540000 z - 2417562987840000 z^2 - 714668258304000 z^3 + 456516639129600 z^4 + 95493449318400 z^5 + 6756017111040 z^6 + 238907555840 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 + (739882875741384375 + 1791716369362920000 z + 222953031100800000 z^2 + 138322888704000 z^3 - 530997755904000 z^4 - 100167214694400 z^5 - 6912548536320 z^6 - 241591910400 z^7 - 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (739882875741384375 + 213299567781300000 z + 8434608646464000 z^2 - 544931380224000 z^3 + 483548921856000 z^4 + 97283683123200 z^5 + 6817421721600 z^6 + 239981297664 z^7 + 4294967296 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (13454736673996800 Sqrt[2] z^(17/4))

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]