Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8436)

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/07.22.03.8436.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(13/4)}, z] == ((4 z (309530265573375 - 81231223134600 z + 92446704345600 z^2 + 53932493260800 z^3 + 11910118440960 z^4 + 1843813416960 z^5 + 426208395264 z^6 - 42916118528 z^7 + 536870912 z^8) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (928590796720125 - 66819231933300 z + 73411565673600 z^2 + 32287239705600 z^3 + 6681473187840 z^4 + 1022176788480 z^5 + 200143798272 z^6 - 21290287104 z^7 + 268435456 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (-2785772390160375 - 330165616611600 z - 154487431375200 z^2 + 450394826112000 z^3 + 231166902067200 z^4 + 49874267013120 z^5 + 7738358759424 z^6 + 1662756323328 z^7 - 171127603200 z^8 + 2147483648 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(197763230808000 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]