Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9998)

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`=1/2

http://functions.wolfram.com/07.22.03.9998.01

Input Form

HypergeometricPFQ[{-(17/4)}, {1/2, 13/4}, z] == ((2 Sqrt[z] (723647925 + 82447485120 z - 360169286400 z^2 + 279765319680 z^3 - 43852038144 z^4 + 1749024768 z^5 - 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (-1206079875 + 5513508000 z + 169870821120 z^2 - 243867402240 z^3 + 42346414080 z^4 - 1734344704 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-3618239625 + 8821612800 z + 188644135680 z^2 - 248547409920 z^3 + 42556784640 z^4 - 1736441856 z^5 + 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (85240995840 Sqrt[2] z^(7/4))

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]