Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8411)

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/07.22.03.8411.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 9/4}, -z] == (Sqrt[Pi] z^(5/4) (-1513180375331625 + 18830689115238000 z + 23176232757216000 z^2 + 5193553559040000 z^3 + 359726653440000 z^4 + 9209002328064 z^5 + 89137348608 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-46888508620800 + 512892191421225 z + 1210918752156960 z^2 + 305469020102400 z^3 + 21963337482240 z^4 + 570401685504 z^5 + 5555355648 z^6 + 16777216 z^7) Cos[2 Sqrt[z]] + 4 (-5861063577600 - 117221271552000 z + 996038817421725 z^2 + 1395575250743520 z^3 + 320604001724160 z^4 + 22377240281088 z^5 + 574524948480 z^6 + 5567938560 z^7 + 16777216 z^8) Sin[2 Sqrt[z]]))/ (22005195551539200 z^(5/2))

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]