Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7tx)

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`=7/2

http://functions.wolfram.com/07.22.03.a7tx.01

Input Form

HypergeometricPFQ[{-(17/4)}, {7/2, 19/4}, -z] == (Sqrt[Pi] (93921540537825 + 1092905198985600 z - 2914413863961600 z^2 + 4441011602227200 z^3 + 8074566549504000 z^4 + 1378059357782016 z^5 + 64470613229568 z^6 + 985694994432 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (31307180179275 - 154562746075920 z + 209777471205120 z^2 + 490015921876992 z^3 + 85397781676032 z^4 + 4017972314112 z^5 + 61555605504 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (-93921540537825 + 16383028137840 z + 18315111709440 z^2 + 436897591603200 z^3 + 82569691201536 z^4 + 3972648665088 z^5 + 61354278912 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (8513621613084672 z^(15/4))

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]