Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ac)

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.a8ac.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, -(13/4)}, z] == ((4 z (236102414625 - 33978760200 z + 29152540800 z^2 + 10994227200 z^3 + 1450475520 z^4 + 112721920 z^5 + 8388608 z^6) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (708307243875 + 32979384900 z + 20540520000 z^2 + 6093849600 z^3 + 767508480 z^4 + 58982400 z^5 + 4194304 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (-2124921731625 - 503685151200 z - 59441104800 z^2 + 131326272000 z^3 + 45665280000 z^4 + 5927731200 z^5 + 459276288 z^6 + 33554432 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(53989416000 Sqrt[2] z^(11/4))

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]