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

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=-9/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(9/2), -(5/2)}, -z] == (1/40186125) (40186125 - 98232750 z + 364864500 z^2 - 5108103000 z^3 - 115783668000 z^4 - 2639867630400 z^5 + 22330308873600 z^6 - 45450614764800 z^7 + 40169121350400 z^8 - 18911133504000 z^9 + 5253528591360 z^10 - 911267481600 z^11 + 101637043200 z^12 - 7351726080 z^13 + 340548480 z^14 - 9685248 z^15 + 153088 z^16 - 1024 z^17) + (1/40186125) ((64 Sqrt[Pi] (114279984000 z^(11/2) - 562609152000 z^(13/2) + 937095868800 z^(15/2) - 746767123200 z^(17/2) + 330964250400 z^(19/2) - 88533648000 z^(21/2) + 14981160600 z^(23/2) - 1643032080 z^(25/2) + 117458505 z^(27/2) - 5395560 z^(29/2) + 152520 z^(31/2) - 2400 z^(33/2) + 16 z^(35/2)) Erfi[Sqrt[z]])/E^z)

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},{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]