Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8467)

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/07.22.03.8467.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 17/4}, -z] == (Sqrt[Pi] z^(1/4) (-12597226624635778125 + 40311125198834490000 z - 57331378060564608000 z^2 + 164643957507262464000 z^3 + 77479509415182336000 z^4 + 8433143881924608000 z^5 + 327103762692833280 z^6 + 5156315471020032 z^7 + 32895154520064 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (3954736715649922125 - 5350223441458526400 z + 7166098459973376000 z^2 + 4414199283037716480 z^3 + 509029313613004800 z^4 + 20149304945541120 z^5 + 320358120947712 z^6 + 2051920625664 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + 4 (-1080311238623232000 + 3291082379575815825 z - 4397643525745008000 z^2 + 9555347421341568000 z^3 + 4751271700882882560 z^4 + 523365341514301440 z^5 + 20384391956004864 z^6 + 321885988454400 z^7 + 2055141851136 z^8 + 4294967296 z^9) Sin[2 Sqrt[z]]))/(146590391042939289600 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]