Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8395)

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`=7/2

http://functions.wolfram.com/07.22.03.8395.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(7/4)}, -z] == (1/(671545274400 z^(5/2))) (2 Sqrt[z] (-135528918525 - 85037752800 z + 43373594880 z^2 - 23040737280 z^3 + 35846553600 z^4 + 5002924032 z^5 + 148242432 z^6 + 1048576 z^7) Cos[2 Sqrt[z]] + 4096 Sqrt[Pi] z^(21/4) (156828375 + 20074032 z + 582912 z^2 + 4096 z^3) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (-135528918525 + 95667471900 z - 130827312000 z^2 + 59087508480 z^3 - 46130135040 z^4 + 313944440832 z^5 + 40891219968 z^6 + 1192230912 z^7 + 8388608 z^8) 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]