Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7wd)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7wd.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 11/4}, -z] == (Sqrt[Pi] z^(11/4) (-5729177010375 + 12222244288800 z + 25731040608000 z^2 + 4773294489600 z^3 + 235718246400 z^4 + 3743416320 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (-126309456000 - 96235776000 z - 269460172800 z^2 + 553910195475 z^3 + 1557734245200 z^4 + 295661882880 z^5 + 14688952320 z^6 + 233766912 z^7 + 1048576 z^8) Cos[2 Sqrt[z]] + (252618912000 - 144353664000 z + 192471552000 z^2 - 19306676025 z^3 + 1375720491600 z^4 + 285348349440 z^5 + 14516920320 z^6 + 232980480 z^7 + 1048576 z^8) Sin[2 Sqrt[z]]))/(26368140902400 z^(9/2))

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]