Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9667)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9667.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 17/4}, -z] == (Sqrt[Pi] z^(5/4) (-109541101083789375 + 173101986897840000 z - 149134019481216000 z^2 + 280722860199936000 z^3 + 89118368317440000 z^4 + 6518372082647040 z^5 + 163470146273280 z^6 + 1509681004544 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-9133066027008000 + 19080256625805375 z - 14388178781869200 z^2 + 13536289898208000 z^3 + 5222705014517760 z^4 + 398159372943360 z^5 + 10129417175040 z^6 + 94103404544 z^7 + 268435456 z^8) Cos[2 Sqrt[z]] + 4 (-1141633253376000 - 9785427886080000 z + 13413727253047275 z^2 - 11097828781578000 z^3 + 16644741775200000 z^4 + 5497470210355200 z^5 + 405520608460800 z^6 + 10199302668288 z^7 + 94304731136 z^8 + 268435456 z^9) Sin[2 Sqrt[z]]))/(226219739263795200 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]