Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9089)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9089.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 15/4}, -z] == (Sqrt[Pi] z^(7/4) (361299089805278625 - 600601084351632000 z + 747414682748697600 z^2 + 1258803676208332800 z^3 + 218922378471014400 z^4 + 11531713763082240 z^5 + 228917394800640 z^6 + 1758789107712 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (5432317083648000 + 16555633016832000 z - 33534357121444725 z^2 + 36123680246799600 z^3 + 76372268504313600 z^4 + 13553108959703040 z^5 + 718093889372160 z^6 + 14286836465664 z^7 + 109873987584 z^8 + 268435456 z^9) Cos[2 Sqrt[z]] + (-10864634167296000 - 18625087143936000 z - 5352979943390625 z^2 + 5893305547474800 z^3 + 68090514191481600 z^4 + 13056291023892480 z^5 + 707715900702720 z^6 + 14205274030080 z^7 + 109672660992 z^8 + 268435456 z^9) Sin[2 Sqrt[z]]))/ (1340230277372313600 z^(9/2))

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]