Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8455)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8455.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 5/4}, -z] == (Sqrt[Pi] z^(13/4) (478527127241625 + 900756945396000 z + 245103930720000 z^2 + 19014123110400 z^3 + 524527534080 z^4 + 5354029056 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 (Sqrt[z] (2943614520000 + 2878200864000 z + 7814751436800 z^2 + 45403180547175 z^3 + 14315413519440 z^4 + 1158849308160 z^5 + 32473128960 z^6 + 333643776 z^7 + 1048576 z^8) Cos[2 Sqrt[z]] - 4 (367951815000 - 130827312000 z + 366316473600 z^2 + 23444254310400 z^3 + 53838917255475 z^4 + 15108803257680 z^5 + 1182370475520 z^6 + 32720658432 z^7 + 334430208 z^8 + 1048576 z^9) Sin[2 Sqrt[z]]))/(649069065216000 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]