Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ak0n)

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=3, a₂>=3

For fixed z and a₁=3, a₂=7/2, b₁>=-11/2

For fixed z and a₁=3, a₂=7/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.ak0n.01

Input Form

HypergeometricPFQ[{3, 7/2}, {-(11/2), -(11/2)}, z] == (1/1620840375) (1620840375 + 562605750 z + 250047000 z^2 + 187110000 z^3 + 291891600 z^4 + 1362160800 z^5 + 61751289600 z^6 + 2258949772800 z^7 + 8249935276800 z^8 + 10085183700480 z^9 + 5747233720320 z^10 + 1772321034240 z^11 + 319197204480 z^12 + 34792611840 z^13 + 2305425408 z^14 + 90054656 z^15 + 1892352 z^16 + 16384 z^17) + (1/1620840375) (4096 E^z Sqrt[Pi] (92534400 z^(13/2) + 1079568000 z^(15/2) + 2855865600 z^(17/2) + 3015532800 z^(19/2) + 1588960800 z^(21/2) + 468024480 z^(23/2) + 81920160 z^(25/2) + 8765280 z^(27/2) + 573615 z^(29/2) + 22215 z^(31/2) + 464 z^(33/2) + 4 z^(35/2)) Erf[Sqrt[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]