Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anbr)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=5, a₂>=5

For fixed z and a₁=5, a₂=11/2, b₁>=-11/2

For fixed z and a₁=5, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.anbr.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(11/2), -(9/2)}, -z] == (1/27848984625) (27848984625 - 30943316250 z + 38310772500 z^2 - 76621545000 z^3 + 347351004000 z^4 - 7919602891200 z^5 - 554372202384000 z^6 + 9198923358240000 z^7 - 29913896965075200 z^8 + 39270950726515200 z^9 - 26637923169285120 z^10 + 10571975927654400 z^11 - 2637957688934400 z^12 + 432182155345920 z^13 - 47653440307200 z^14 + 3572331227136 z^15 - 181346088960 z^16 + 6102666240 z^17 - 129705984 z^18 + 1568768 z^19 - 8192 z^20) + (1/27848984625) ((512 Sqrt[Pi] (4061334816000 z^(13/2) - 33302945491200 z^(15/2) + 83719241020800 z^(17/2) - 96329497017600 z^(19/2) + 60517451332800 z^(21/2) - 22893033240000 z^(23/2) + 5535094007520 z^(25/2) - 887546555280 z^(27/2) + 96398427510 z^(29/2) - 7148648430 z^(31/2) + 360028305 z^(33/2) - 12044424 z^(35/2) + 254856 z^(37/2) - 3072 z^(39/2) + 16 z^(41/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 96329497017600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 83719241020800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 33302945491200 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4061334816000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},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]