Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8491)

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`=11/2

http://functions.wolfram.com/07.22.03.8491.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(7/4)}, -z] == (2 Sqrt[z] (-2490343877896875 + 493325263431000 z + 34695403142400 z^2 - 27212080896000 z^3 + 8005330206720 z^4 - 3472057958400 z^5 + 4929229946880 z^6 + 510472224768 z^7 + 11802771456 z^8 + 67108864 z^9) Cos[2 Sqrt[z]] + 262144 Sqrt[Pi] z^(29/4) (328149855 + 31820592 z + 724224 z^2 + 4096 z^3) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (-2490343877896875 + 3813783767293500 z + 262383986264400 z^2 + 88439262912000 z^3 - 29305317888000 z^4 + 9657353502720 z^5 - 6578236293120 z^6 + 42266806714368 z^7 + 4153210306560 z^8 + 94824824832 z^9 + 536870912 z^10) Sin[2 Sqrt[z]])/ (258726141273600 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]