Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7um)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7um.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, -(3/4)}, z] == (1/(4345335720 Sqrt[2] z^(9/4))) ((4 z (890127225 + 1721204640 z - 1285574400 z^2 - 7935344640 z^3 + 2953863168 z^4 - 174063616 z^5 + 2097152 z^6) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (1483545375 - 620568000 z - 2428600320 z^2 - 2796994560 z^3 + 1402327040 z^4 - 86114304 z^5 + 1048576 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (22253180625 - 7330459500 z + 6129302400 z^2 + 19214115840 z^3 + 23539875840 z^4 - 11301519360 z^5 + 689963008 z^6 - 8388608 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]