Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0486)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=-1/2

http://functions.wolfram.com/07.22.03.0486.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(1/2), 5/2}, -z] == (1/(645120 z^(3/2))) (-2 Sqrt[z] (31185 - 125055 z + 613242 z^2 + 279465 z^3 + 24646 z^4 + 614 z^5 + 4 z^6) Cos[2 Sqrt[z]] - (-31185 - 155925 z + 435330 z^2 + 257943 z^3 + 24054 z^4 + 610 z^5 + 4 z^6) Sin[2 Sqrt[z]] - 8 z^3 (363825 + 145530 z + 12474 z^2 + 308 z^3 + 2 z^4) SinIntegral[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]