Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8031)

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/07.22.03.8031.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 13/4}, -z] == (Sqrt[Pi] (309530265573375 + 293480548099200 z + 714561334502400 z^2 - 401157240422400 z^3 + 76410902937600 z^4 - 8083136839680 z^5 + 615858044928 z^6 - 49392123904 z^7 - 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-(309530265573375 - 36685068512400 z + 30787663092480 z^2 - 5352089702400 z^3 + 543820677120 z^4 - 40394293248 z^5 + 2835349504 z^6 + 268435456 z^7)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-103176755191125 - 50660332707600 z + 26200531848960 z^2 - 4885724712960 z^3 + 512998047744 z^4 - 38959841280 z^5 + 3036676096 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (909158677217280 z^(9/4))

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]