Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8rd)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8rd.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, 23/4}, -z] == (Sqrt[Pi] (-82871947533375 - 707173952284800 z + 1200052767513600 z^2 - 783707929804800 z^3 + 474974502912000 z^4 + 405311575818240 z^5 + 34131501121536 z^6 + 753766760448 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-27623982511125 + 73699117455600 z - 48282045477120 z^2 + 25699858329600 z^3 + 24950636347392 z^4 + 2124495716352 z^5 + 47060090880 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (82871947533375 + 25185884396400 z - 32429446882560 z^2 + 12398639984640 z^3 + 23497128345600 z^4 + 2090043703296 z^5 + 46858764288 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (512097540636672 z^(19/4))

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]