Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8fd)

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.a8fd.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(9/2), 23/4}, -z] == -((209 (Sqrt[Pi] (74949174425750625 + 17285575363056000 z + 2666645235072000 z^2 + 420357869568000 z^3 + 112095431884800 z^4 - 68324834672640 z^5 + 6430572675072 z^6 - 251255586816 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (24983058141916875 - 5658968124810000 z + 100679462956800 z^2 + 8019648000000 z^3 - 4352782565376 z^4 + 404965294080 z^5 - 15753805824 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (-74949174425750625 + 62660210691078000 z - 4532389877433600 z^2 + 13152222720000 z^3 - 4713917644800 z^4 + 417623703552 z^5 - 15955132416 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (26599385299156992 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]