Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1337)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=11/2

http://functions.wolfram.com/07.22.03.1337.01

Input Form

HypergeometricPFQ[{-(7/2)}, {11/2, 6}, z] == (1/(50185175040 z^(9/2))) (4 (2 Sqrt[z] (52022476800 + 120468377925 z + 72386225100 z^2 + 27365461200 z^3 + 18355296960 z^4 - 5053257984 z^5 + 256869376 z^6 - 3903488 z^7 + 16384 z^8) BesselI[0, 2 Sqrt[z]] - (104044953600 + 166320845775 z + 88925312700 z^2 + 33103047600 z^3 + 16036574400 z^4 - 4928164608 z^5 + 254931968 z^6 - 3895296 z^7 + 16384 z^8) BesselI[1, 2 Sqrt[z]]) - Pi Sqrt[z] (379915160625 + 578918340000 z + 324194270400 z^2 + 123502579200 z^3 + 68612544000 z^4 - 19960012800 z^5 + 1023590400 z^6 - 15597568 z^7 + 65536 z^8) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi Sqrt[z] (379915160625 + 578918340000 z + 324194270400 z^2 + 123502579200 z^3 + 68612544000 z^4 - 19960012800 z^5 + 1023590400 z^6 - 15597568 z^7 + 65536 z^8) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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</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]