Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8371)

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`=5/2

http://functions.wolfram.com/07.22.03.8371.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 17/4}, -z] == (Sqrt[Pi] (30951416768146875 + 165074222763450000 z - 2112950051372160000 z^2 + 15776693716912128000 z^3 + 14023727748366336000 z^4 + 2465710373339136000 z^5 + 140646581010432000 z^6 + 3061694280499200 z^7 + 25782688677888 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-30951416768146875 - 132059378210760000 z + 524710042195046400 z^2 + 758934524668723200 z^3 + 146521354585374720 z^4 + 8616821863219200 z^5 + 189861042585600 z^6 + 1607391510528 z^7 + 4294967296 z^8)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (10317138922715625 - 169183472655859200 z + 867595448877696000 z^2 + 850754911297536000 z^3 + 152533225346826240 z^4 + 8755182116536320 z^5 + 191055513255936 z^6 + 1610612736000 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/ (16808071045054464000 z^(13/4))

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]