Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa5x)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.aa5x.01

Input Form

HypergeometricPFQ[{-(5/4)}, {-(11/2), 19/4}, -z] == (1/(51539607552 z^(15/4))) (-663 Sqrt[Pi] (21471132375 + 4220370000 z + 584640000 z^2 + 107520000 z^3 - 34406400 z^4 + 1048576 z^5) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) (4 Sqrt[z] (4745120254875 - 1236496060800 z + 53404915200 z^2 - 1601634304 z^3 + 43450368 z^4) Cos[2 Sqrt[z]] + 51 (-279124720875 + 242868225600 z - 24692595200 z^2 + 306790400 z^3 + 851968 z^4) Sin[2 Sqrt[z]]))

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]