Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9192)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.9192.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 23/4}, z] == ((2 Sqrt[z] (-14057774639086303125 - 12215970960503310000 z + 173527298904960000 z^2 - 68331507019776000 z^3 + 48869070579302400 z^4 + 12870813273292800 z^5 + 1215711632424960 z^6 + 64488933949440 z^7 + 2314987372544 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]]^2 - (-42173323917258909375 - 100912025517333030000 z - 9921678502095360000 z^2 + 23653213968384000 z^3 + 60302699347968000 z^4 + 13776612124262400 z^5 + 1260705105838080 z^6 + 66051228303360 z^7 + 2357937045504 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (42173323917258909375 + 10942267827180690000 z + 287851166418816000 z^2 - 46266726223872000 z^3 + 52746174480384000 z^4 + 13205474692300800 z^5 + 1232864658063360 z^6 + 65094524338176 z^7 + 2332167241728 z^8 + 68719476736 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(80728420043980800 Sqrt[2] z^(17/4))

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]