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

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=-11/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(11/2), -(11/2)}, z] == (1/1531694154375) (1531694154375 + 1670939077500 z + 1877227852500 z^2 + 3064861800000 z^3 + 9378477108000 z^4 + 79196028912000 z^5 + 6098094226224000 z^6 + 385225729967232000 z^7 + 2460095352326304000 z^8 + 5340039935071564800 z^9 + 5556034824633216000 z^10 + 3260676441673728000 z^11 + 1184135238287769600 z^12 + 281830054573670400 z^13 + 45598884643307520 z^14 + 5128981242255360 z^15 + 405612310763520 z^16 + 22574241592320 z^17 + 874922081280 z^18 + 23006035968 z^19 + 389595136 z^20 + 3817472 z^21 + 16384 z^22) + (1/1531694154375) (512 E^z Sqrt[Pi] (93410700768000 z^(13/2) + 1774803314592000 z^(15/2) + 7821772502544000 z^(17/2) + 14171000980752000 z^(19/2) + 13304493822312000 z^(21/2) + 7327729982865600 z^(23/2) + 2553105496788000 z^(25/2) + 590789641226400 z^(27/2) + 93721096611450 z^(29/2) + 10393546189950 z^(31/2) + 813455094375 z^(33/2) + 44923182255 z^(35/2) + 1730927730 z^(37/2) + 45310440 z^(39/2) + 764640 z^(41/2) + 7472 z^(43/2) + 32 z^(45/2)) 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]