Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0945)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=3

http://functions.wolfram.com/07.22.03.0945.01

Input Form

HypergeometricPFQ[{-(9/2)}, {3, 7/2}, z] == (1/(23247544320 z^2)) (-4 (2 z (-481935825 - 4626583920 z + 4986073008 z^2 - 920060928 z^3 + 48641280 z^4 - 839680 z^5 + 4096 z^6) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (836169075 + 2756867400 z - 4565007216 z^2 + 896456448 z^3 - 48225024 z^4 + 837632 z^5 - 4096 z^6) BesselI[1, 2 Sqrt[z]]) + Pi (-383107725 - 3575672100 z - 14302688400 z^2 + 19070251200 z^3 - 3632428800 z^4 + 193729536 z^5 - 3354624 z^6 + 16384 z^7) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (383107725 + 3575672100 z + 14302688400 z^2 - 19070251200 z^3 + 3632428800 z^4 - 193729536 z^5 + 3354624 z^6 - 16384 z^7) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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</ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3575672100 </cn> <ci> z </ci> </apply> <cn type='integer'> 383107725 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> StruveL </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]