Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8444)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8444.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(5/4)}, z] == ((4 z (17445345080625 - 8604621333000 z + 21455273347200 z^2 + 29614717440000 z^3 + 38124011520000 z^4 - 16823776542720 z^5 + 1227775016960 z^6 - 25006440448 z^7 + 134217728 z^8) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (52336035241875 - 15845095381500 z + 14561079825600 z^2 + 18011843942400 z^3 + 14700736512000 z^4 - 8048429383680 z^5 + 606185717760 z^6 - 12461277184 z^7 + 67108864 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (-157008105725625 + 17628980292000 z - 33075324928800 z^2 + 114534950745600 z^3 + 137648454451200 z^4 + 137416546713600 z^5 - 66105415434240 z^6 + 4886303342592 z^7 - 99891544064 z^8 + 536870912 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (59159940840000 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]