Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a88n)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a88n.01

Input Form

HypergeometricPFQ[{-(15/4)}, {5/2, 21/4}, -z] == (Sqrt[Pi] (8890014758625 + 12504636144000 z + 25935541632000 z^2 - 165987466444800 z^3 + 663949865779200 z^4 + 314761417850880 z^5 + 27671333437440 z^6 + 676457349120 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-8890014758625 - 3021953734800 z - 15005563372800 z^2 + 28184241254400 z^3 + 18198432645120 z^4 + 1690813071360 z^5 + 42026926080 z^6 + 268435456 z^7)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (2963338252875 + 2813543132400 z - 13335071904000 z^2 + 38418610728960 z^3 + 19364974755840 z^4 + 1721641205760 z^5 + 42228252672 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (606105784811520 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]