Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7099)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-23/4

http://functions.wolfram.com/07.22.03.7099.01

Input Form

HypergeometricPFQ[{4}, {-(23/4), 23/4}, -z] == (1/(2260992 z^(19/4))) (4 z^(3/4) (5293484571375 - 1411595885700 z + 163199836800 z^2 - 9625936320 z^3 + 311377152 z^4 - 4850688 z^5 + 16384 z^6) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-15880453714125 + 31458422595600 z - 9980552181600 z^2 + 1207004198400 z^3 - 72890737920 z^4 + 2398556160 z^5 - 38019072 z^6 + 131072 z^7) Cos[2 Sqrt[z]] - 6 Sqrt[z] (5293484571375 - 3428161436700 z + 638096659200 z^2 - 53439946560 z^3 + 2379336960 z^4 - 56376320 z^5 + 507904 z^6) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (6 Sqrt[z] (5293484571375 - 3428161436700 z + 638096659200 z^2 - 53439946560 z^3 + 2379336960 z^4 - 56376320 z^5 + 507904 z^6) Cos[2 Sqrt[z]] + (-15880453714125 + 31458422595600 z - 9980552181600 z^2 + 1207004198400 z^3 - 72890737920 z^4 + 2398556160 z^5 - 38019072 z^6 + 131072 z^7) 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]