Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a98g)

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

For fixed z and a₁=-11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a98g.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, 15/4}, z] == -(((2 z (-1344697200 - 8329045725 z - 7062778800 z^2 - 13419118080 z^3 + 2847416320 z^4 - 115146752 z^5 + 1048576 z^6) BesselI[-(1/4), Sqrt[z]]^ 2 + Sqrt[z] (8068183200 + 16534754775 z + 11842815600 z^2 + 11820695040 z^3 - 2777210880 z^4 + 114491392 z^5 - 1048576 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 (-3025568700 + 6339286800 z + 11895986025 z^2 + 9497703600 z^3 + 12750312960 z^4 - 2819039232 z^5 + 114884608 z^6 - 1048576 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(14766336000 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]