Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8495)

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`=11/2

http://functions.wolfram.com/07.22.03.8495.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(3/4)}, -z] == (-2 Sqrt[z] (99613755115875 - 10842313482000 z + 425188764000 z^2 + 3663164736000 z^3 - 3004273704960 z^4 + 5649558405120 z^5 + 1286517980160 z^6 + 64257048576 z^7 + 984875008 z^8 + 4194304 z^9) Cos[2 Sqrt[z]] - 1024 Sqrt[Pi] z^(25/4) (104679803745 + 21001590720 z + 1018258944 z^2 + 15450112 z^3 + 65536 z^4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (99613755115875 - 143660653636500 z - 20536617301200 z^2 - 6541365600000 z^3 + 6512292864000 z^4 - 6738308628480 z^5 + 51774703534080 z^6 + 10658220957696 z^7 + 519879131136 z^8 + 7904165888 z^9 + 33554432 z^10) Sin[2 Sqrt[z]])/ (36960877324800 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]