Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9026)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9026.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 1/4}, z] == ((4 z (69272842275 + 1537703319600 z - 10575549734400 z^2 + 10032664199040 z^3 - 1892295659520 z^4 + 101088755712 z^5 - 1739587584 z^6 + 8388608 z^7) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (115454737125 - 88416619200 z - 2020798886400 z^2 + 4257687067200 z^3 - 903178321920 z^4 + 49789501440 z^5 - 866123776 z^6 + 4194304 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (1731821056875 - 1172309638500 z + 1503082526400 z^2 + 18590923008000 z^3 - 34831639180800 z^4 + 7272664842240 z^5 - 399169290240 z^6 + 6933184512 z^7 - 33554432 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(3193821754200 Sqrt[2] z^(9/4))

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]