Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0612)

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

For fixed z and a₁=-11/2, b₁=3

http://functions.wolfram.com/07.22.03.0612.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3, 11/2}, -z] == (1/(510117543936000 z^4)) (4 (2 z (2212447111875 + 3624199078500 z - 27087091416000 z^2 + 114792134688000 z^3 + 94090311590400 z^4 + 14564483020800 z^5 + 734175313920 z^6 + 14260174848 z^7 + 108199936 z^8 + 262144 z^9) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (6637341335625 + 9692625442500 z - 42037330104000 z^2 + 77790458592000 z^3 + 87391102348800 z^4 + 14209396070400 z^5 + 727138713600 z^6 + 14206304256 z^7 + 108068864 z^8 + 262144 z^9) BesselJ[1, 2 Sqrt[z]]) + Pi (6637341335625 + 12642554925000 z + 45513197730000 z^2 - 161824703040000 z^3 + 377590973760000 z^4 + 362487334809600 z^5 + 57537672192000 z^6 + 2922548428800 z^7 + 56932761600 z^8 + 432537600 z^9 + 1048576 z^10) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (6637341335625 + 12642554925000 z + 45513197730000 z^2 - 161824703040000 z^3 + 377590973760000 z^4 + 362487334809600 z^5 + 57537672192000 z^6 + 2922548428800 z^7 + 56932761600 z^8 + 432537600 z^9 + 1048576 z^10) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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</mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1048576 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 432537600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 56932761600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2922548428800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 57537672192000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 362487334809600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 377590973760000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 161824703040000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> 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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]