Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a89z)

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`=7/2

http://functions.wolfram.com/07.22.03.a89z.01

Input Form

HypergeometricPFQ[{-(15/4)}, {7/2, 21/4}, -z] == (Sqrt[Pi] (-31750052709375 - 104205301200000 z + 648388540800000 z^2 - 829937332224000 z^3 + 1844305182720000 z^4 + 605310418944000 z^5 + 40693137408000 z^6 + 805306368000 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((31750052709375 + 70338578310000 z - 81247013971200 z^2 + 87670704844800 z^3 + 35624476016640 z^4 + 2497126072320 z^5 + 50079989760 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] - 4 Sqrt[z] (-10583350903125 + 53814599823600 z - 63032445907200 z^2 + 109099320422400 z^3 + 37374991073280 z^4 + 2533994004480 z^5 + 50281316352 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (1515264462028800 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]