Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a94n)

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

For fixed z and a₁=-11/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a94n.01

Input Form

HypergeometricPFQ[{-(11/4)}, {5/2, 21/4}, -z] == (1/(901943132160 z^(17/4))) (Sqrt[Pi] (28222269075 + 34735100400 z + 61751289600 z^2 - 329340211200 z^3 + 1053888675840 z^4 + 374715973632 z^5 + 21961375744 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((28222269075 + 4631346720 z + 32345913600 z^2 - 48425287680 z^3 - 22194880512 z^4 - 1356857344 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (9407423025 + 7277830560 z - 26292752640 z^2 + 61997236224 z^3 + 23169269760 z^4 + 1369440256 z^5 + 16777216 z^6) 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]