Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7v1)

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.a7v1.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 11/4}, -z] == (7 (Sqrt[Pi] z^(7/4) (-1800598488975 + 5238104695200 z + 13968279187200 z^2 + 3136736378880 z^3 + 181839790080 z^4 + 3315597312 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (-20621952000 - 71489433600 z + 221012458875 z^2 + 840426768720 z^3 + 193997422080 z^4 + 11326562304 z^5 + 207028224 z^6 + 1048576 z^7) Cos[2 Sqrt[z]] + (41243904000 + 87986995200 z - 47128410225 z^2 + 724891686480 z^3 + 186121704960 z^4 + 11174584320 z^5 + 206241792 z^6 + 1048576 z^7) Sin[2 Sqrt[z]])))/(94925307248640 z^(7/2))

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]