Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ans7)

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=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.ans7.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(9/2), -(9/2)}, -z] == (1/12658629375) (12658629375 - 20628877500 z + 38310772500 z^2 - 122594472000 z^3 + 1042053012000 z^4 - 79196028912000 z^5 + 4869355838256000 z^6 - 29927360905344000 z^7 + 61932968371411200 z^8 - 60881957594035200 z^9 + 33445211700096000 z^10 - 11254149056102400 z^11 + 2453265548697600 z^12 - 358582045409280 z^13 + 35826623239680 z^14 - 2462833013760 z^15 + 115734961920 z^16 - 3633070080 z^17 + 72486912 z^18 - 827392 z^19 + 4096 z^20) - (1/12658629375) ((128 Sqrt[Pi] (-4799759328000 z^(11/2) + 88610941440000 z^(13/2) - 376042682736000 z^(15/2) + 650327571936000 z^(17/2) - 577666580904000 z^(19/2) + 298206680889600 z^(21/2) - 96383053116000 z^(23/2) + 20447329089600 z^(25/2) - 2932760183850 z^(27/2) + 289096844400 z^(29/2) - 19679459625 z^(31/2) + 918095850 z^(33/2) - 28663320 z^(35/2) + 569520 z^(37/2) - 6480 z^(39/2) + 32 z^(41/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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/> 2 </cn> </apply> </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> </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]