Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9om)

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`=11/2

http://functions.wolfram.com/07.22.03.a9om.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, 21/4}, z] == -((17 (2 Sqrt[z] (-215251811775 - 257681904480 z - 114329698560 z^2 - 79256567808 z^3 + 33817559040 z^4 - 1667235840 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (358753019625 + 348713164800 z + 143463640320 z^2 + 52018053120 z^3 - 32383500288 z^4 + 1652555776 z^5 - 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (422421874875 + 353188836000 z + 145104410880 z^2 + 55484006400 z^3 - 32583647232 z^4 + 1654652928 z^5 - 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (654950596608 Sqrt[2] z^(15/4)))

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]