Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an1k)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.an1k.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(9/2), -(9/2)}, z] == (1/1406514375) (1406514375 + 1875352500 z + 2946982500 z^2 + 8172964800 z^3 + 61297236000 z^4 + 4168212048000 z^5 + 228948519945600 z^6 + 1256601606220800 z^7 + 2320292270096640 z^8 + 2028915045964800 z^9 + 986189391129600 z^10 + 291370967838720 z^11 + 55183460290560 z^12 + 6908988248064 z^13 + 579960017280 z^14 + 32601260160 z^15 + 1203795456 z^16 + 27859968 z^17 + 364544 z^18 + 2048 z^19) + (1/1406514375) (64 E^z Sqrt[Pi] (479975932800 z^(11/2) + 8011905955200 z^(13/2) + 30669231398400 z^(15/2) + 47666026195200 z^(17/2) + 37857182479200 z^(19/2) + 17356633227360 z^(21/2) + 4939151243040 z^(23/2) + 912245755680 z^(25/2) + 112250801565 z^(27/2) + 9307686465 z^(29/2) + 518588658 z^(31/2) + 19024152 z^(33/2) + 438144 z^(35/2) + 5712 z^(37/2) + 32 z^(39/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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</apply> <apply> <times /> <cn type='integer'> 479975932800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Erf </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]