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

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.anbt.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(11/2), -(7/2)}, -z] == (1/3094331625) (3094331625 - 4420473750 z + 7662154500 z^2 - 25540515000 z^3 + 347351004000 z^4 + 7919602891200 z^5 + 184790734128000 z^6 - 1631844329068800 z^7 + 3510965929363200 z^8 - 3321019082304000 z^9 + 1695467133803520 z^10 - 518393656166400 z^11 + 100736468582400 z^12 - 12870586552320 z^13 + 1098475499520 z^14 - 62617729536 z^15 + 2340149760 z^16 - 54733824 z^17 + 722944 z^18 - 4096 z^19) + (1/3094331625) ((256 Sqrt[Pi] (-2030667408000 z^(13/2) + 10424092694400 z^(15/2) - 18323787081600 z^(17/2) + 15601141987200 z^(19/2) - 7486051557600 z^(21/2) + 2200997383200 z^(23/2) - 416762078040 z^(25/2) + 52309386360 z^(27/2) - 4408904115 z^(29/2) + 249067665 z^(31/2) - 9246720 z^(33/2) + 215208 z^(35/2) - 2832 z^(37/2) + 16 z^(39/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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</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]