Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1637)

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=-5/2, b_1`>=-11/2

For fixed z and a₁=-5/2, b₁=3

http://functions.wolfram.com/07.22.03.1637.01

Input Form

HypergeometricPFQ[{-(5/2)}, {3, 11/2}, z] == (1/(41287680 z^4)) (-4 (2 z (1488375 - 1587600 z - 6042960 z^2 - 11796480 z^3 + 5160192 z^4 - 323584 z^5 + 4096 z^6) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (-4465125 + 3969000 z + 8683920 z^2 + 9480960 z^3 - 5001984 z^4 + 321536 z^5 - 4096 z^6) BesselI[1, 2 Sqrt[z]]) + Pi (-4465125 + 5953500 z - 14288400 z^2 - 31752000 z^3 - 42336000 z^4 + 20321280 z^5 - 1290240 z^6 + 16384 z^7) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (4465125 - 5953500 z + 14288400 z^2 + 31752000 z^3 + 42336000 z^4 - 20321280 z^5 + 1290240 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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type='integer'> 5953500 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 4465125 </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]