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

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.anbp.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(11/2), -(11/2)}, -z] == (1/306338830875) (306338830875 - 278489846250 z + 268175407500 z^2 - 383107725000 z^3 + 1042053012000 z^4 - 7919602891200 z^5 + 554372202384000 z^6 - 31755576926304000 z^7 + 183671701008364800 z^8 - 360625157890905600 z^9 + 338382713469588480 z^10 - 178261605368985600 z^11 + 57735915993907200 z^12 - 12150668593889280 z^13 + 1718956157829120 z^14 - 166586283085824 z^15 + 11128483860480 z^16 - 509030307840 z^17 + 15576139776 z^18 - 303329280 z^19 + 3383296 z^20 - 16384 z^21) + (1/306338830875) ((1024 Sqrt[Pi] (-4061334816000 z^(13/2) + 70667225798400 z^(15/2) - 284460668553600 z^(17/2) + 469037229091200 z^(19/2) - 398916753681600 z^(21/2) + 197875650772800 z^(23/2) - 61638691292640 z^(25/2) + 12635466449760 z^(27/2) - 1755132402870 z^(29/2) + 167884911810 z^(31/2) - 11108959785 z^(33/2) + 504561393 z^(35/2) - 15357552 z^(37/2) + 297864 z^(39/2) - 3312 z^(41/2) + 16 z^(43/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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<power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4061334816000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 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> </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]